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9. Sequences, Series, & Induction

Arithmetic Sequences

9. Sequences, Series, & Induction

Arithmetic Sequences

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Arithmetic Sequences - Recursive Formula

Arithmetic Sequences - Recursive Formula

Arithmetic Sequences - General Formula

Arithmetic Sequences - General Formula

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Quick Intro to Arithmetic Sequences

Quick Intro to Arithmetic Sequences

Quick Intro to Arithmetic Sequences

Quick Intro to Arithmetic Sequences

Arithmetic Sequences: A Formula for the ' n - th ' Term

Arithmetic Sequences: A Formula for the ' n - th ' Term

Arithmetic Sequences: Finding a General Formula Given Two Terms

Arithmetic Sequences: Finding a General Formula Given Two Terms

Arithmetic Sequences: A Formula for the ' n - th ' Term

Arithmetic Sequences: A Formula for the ' n - th ' Term

Finding the Sum of a Finite Arithmetic Series

Finding the Sum of a Finite Arithmetic Series

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Multiple Choice

Write a recursive formula for the arithmetic sequence.

$\left\lbrace8,2,-4,-10,\ldots\right\rbrace$

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Multiple Choice

Find the general formula for the arithmetic sequence below. Without using a recursive formula, calculate the $30^{\th}$ term.

$\left\lbrace-9,-4,1,6,\ldots\right\rbrace$

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Textbook Question

In Exercises 1–14, write the first six terms of each arithmetic sequence. a₁ = 200, d = 20

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Textbook Question

In Exercises 1–14, write the first six terms of each arithmetic sequence. a₁ = 200, d = 20

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Textbook Question

In Exercises 1–14, write the first six terms of each arithmetic sequence. a1= -8, d=5

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Textbook Question

In Exercises 1–14, write the first six terms of each arithmetic sequence. a1= -8, d=5

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Textbook Question

In Exercises 1–14, write the first six terms of each arithmetic sequence. a1 = 300, d= -90

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Textbook Question

In Exercises 1–14, write the first six terms of each arithmetic sequence. a1= 5/2, d = -1/2

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Textbook Question

In Exercises 1–14, write the first six terms of each arithmetic sequence. a1= 5/2, d = -1/2

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Textbook Question

In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 +6, a₁ = −9

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Textbook Question

In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 +6, a₁ = −9

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Textbook Question

In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 -10, a₁ = 30

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Textbook Question

In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 -10, a₁ = 30

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Textbook Question

In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 -0.4, a₁ = 1.6

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Textbook Question

In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 -0.4, a₁ = 1.6

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Textbook Question

In Exercises 12–15, write the first six terms of each arithmetic sequence. a1 = 3/2, d = -1/2

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Textbook Question

In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a6 when a₁ = 13, d = 4.

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Textbook Question

In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a6 when a₁ = 13, d = 4.

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Textbook Question

In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a50 when a₁ = 7, d = 5.

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Textbook Question

In Exercises 16–18, find the indicated term of the arithmetic sequence with first term, , and common difference, d. Find a12 when a1 = -8, d = -2

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Textbook Question

In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a50 when a₁ = 7, d = 5.

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Textbook Question

In Exercises 16–18, find the indicated term of the arithmetic sequence with first term, , and common difference, d. Find a12 when a1 = -8, d = -2

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Textbook Question

In Exercises 16–18, find the indicated term of the arithmetic sequence with first term, , and common difference, d. Find a12 when a1 = -8, d = -2

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Textbook Question

In Exercises 19–21, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence. -7, -3, 1, 5 ...

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Textbook Question

In Exercises 19–21, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence. -7, -3, 1, 5 ...

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Textbook Question

In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a200 when a₁ = −40, d = 5.

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Textbook Question

In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a200 when a₁ = −40, d = 5.

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Textbook Question

In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a60 when a₁ = 35, d = -3.

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Textbook Question

Find the sum of the first 22 terms of the arithmetic sequence: 5, 12, 19, 26, ...

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Textbook Question

Find the sum of the first 22 terms of the arithmetic sequence: 5, 12, 19, 26, ...

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Textbook Question

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. 1, 5, 9, 13,...

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Textbook Question

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. 1, 5, 9, 13,...

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Textbook Question

Find 3 + 6 + 9 + ... + 300, the sum of the first 100 positive multiples of 3.

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Textbook Question

Find 3 + 6 + 9 + ... + 300, the sum of the first 100 positive multiples of 3.

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Textbook Question

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. 7,3,-1,-5,...

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Textbook Question

In Exercises 25–27, use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. The is a summation, refer to the textbook.

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Textbook Question

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. 7,3,-1,-5,...

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Textbook Question

In Exercises 25–27, use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. The is a summation, refer to the textbook.

Has a video solution.

Textbook Question

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. a1 = 9, d=2

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Textbook Question

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. a1 = 9, d=2

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Textbook Question

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. a1=-20, d = -4

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Textbook Question

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. a1=-20, d = -4

Has a video solution.

Textbook Question

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. an = an-1 +3, a₁ = 4

Has a video solution.

Textbook Question

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. an = an-1 +3, a₁ = 4

Has a video solution.

Textbook Question

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. an= an-1 -10, a₁ = 30

Has a video solution.

Textbook Question

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. an= an-1 -10, a₁ = 30

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Textbook Question

Find the sum of the first 20 terms of the arithmetic sequence: 4, 10, 16, 22,……….

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Textbook Question

Find the sum of the first 20 terms of the arithmetic sequence: 4, 10, 16, 22,……….

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Textbook Question

Find the sum of the first 50 terms of the arithmetic sequence: -10, -6, -2, 2,....

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Textbook Question

Find the sum of the first 50 terms of the arithmetic sequence: -10, -6, -2, 2,....

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Textbook Question

Find 1+2+3+4+...+ 100, the sum of the first 100 natural numbers.

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Textbook Question

Find 1+2+3+4+...+ 100, the sum of the first 100 natural numbers.

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Textbook Question

Find the sum of the first 60 positive even integers.

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Textbook Question

Find the sum of the first 60 positive even integers.

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Textbook Question

Find the sum of the even integers between 21 and 45.

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Textbook Question

Find the sum of the even integers between 21 and 45.

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Textbook Question

Find the sum of the even integers between 21 and 45.

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Textbook Question

Find the sum of the odd integers between 30 and 54.

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Textbook Question

For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

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Textbook Question

For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

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Textbook Question

For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

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Textbook Question

For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

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Textbook Question

For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

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Textbook Question

For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

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Textbook Question

For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

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Textbook Question

Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58.

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Textbook Question

Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58.

If {a} is a finite sequence whose last term is -83, how many terms does {a} contain?

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Textbook Question

Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58.

Find the difference between the sum of the first 14 terms of {b} and the sum of the first 14 terms of {an}.

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Textbook Question

Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58.

Find the difference between the sum of the first 14 terms of {b} and the sum of the first 14 terms of {an}.

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Textbook Question

In the sequence 21,700, 23,172, 24,644, 26,116,... which term is 314,628?

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Textbook Question

Show that the sum of the first n positive odd integers,1 +3 +5 + ··· + (2n − 1), ... is n².

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Textbook Question

Use the formula a_n=4+(n-1)(-7) to find the eighth term of the sequence 4, −3, −10,…

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Textbook Question

Use the formula a_n=4+(n-1)(-7) to find the eighth term of the sequence 4, −3, −10,…

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