9. Sequences, Series, & Induction

Arithmetic Sequences

9. Sequences, Series, & Induction

# Arithmetic Sequences - Video Tutorials & Practice Problems

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concept

## Arithmetic Sequences - Recursive Formula

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Problem

ProblemWrite a recursive formula for the arithmetic sequence.

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

A

$a_{n}=a_{n-1}-10$ ; $a_1=6$

B

$a_{n}=a_{n-1}-6$ ; $a_1=6$

C

$a_{n}=a_{n-1}-6$ ; $a_1=8$

D

$a_{n}=a_{n-1}-10$ ; $a_1=8$

3

concept

## Arithmetic Sequences - General Formula

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4

Problem

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

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

A

46

B

136

C

146

D

150

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example

## Example 2

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PRACTICE PROBLEMS AND ACTIVITIES (71)

- In Exercises 1–14, write the first six terms of each arithmetic sequence. a₁ = 200, d = 20
- In Exercises 1–14, write the first six terms of each arithmetic sequence. a₁ = 200, d = 20
- In Exercises 1–14, write the first six terms of each arithmetic sequence. a1= -8, d=5
- In Exercises 1–14, write the first six terms of each arithmetic sequence. a1= -8, d=5
- In Exercises 1–14, write the first six terms of each arithmetic sequence. a1 = 300, d= -90
- In Exercises 1–14, write the first six terms of each arithmetic sequence. a1= 5/2, d = -1/2
- In Exercises 1–14, write the first six terms of each arithmetic sequence. a1= 5/2, d = -1/2
- In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 +6, a₁ = −9
- In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 +6, a₁ = −9
- In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 -10, a₁ = 30
- In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 -10, a₁ = 30
- In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 -0.4, a₁ = 1.6
- In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 -0.4, a₁ = 1.6
- In Exercises 12–15, write the first six terms of each arithmetic sequence. a1 = 3/2, d = -1/2
- In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, and common difference,...
- In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, and common difference,...
- In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, and common difference,...
- In Exercises 16–18, find the indicated term of the arithmetic sequence with first term, , and common differenc...
- In Exercises 16–18, find the indicated term of the arithmetic sequence with first term, , and common differenc...
- In Exercises 16–18, find the indicated term of the arithmetic sequence with first term, , and common differenc...
- In Exercises 19–21, write a formula for the general term (the nth term) of each arithmetic sequence. Do not us...
- In Exercises 19–21, write a formula for the general term (the nth term) of each arithmetic sequence. Do not us...
- Find the sum of the first 22 terms of the arithmetic sequence: 5, 12, 19, 26, ...
- Find the sum of the first 22 terms of the arithmetic sequence: 5, 12, 19, 26, ...
- In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not us...
- In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not us...
- Find 3 + 6 + 9 + ... + 300, the sum of the first 100 positive multiples of 3.
- Find 3 + 6 + 9 + ... + 300, the sum of the first 100 positive multiples of 3.
- In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not us...
- In Exercises 25–27, use the formula for the sum of the first n terms of an arithmetic sequence to find the ind...
- In Exercises 25–27, use the formula for the sum of the first n terms of an arithmetic sequence to find the ind...
- Find the sum of the first 20 terms of the arithmetic sequence: 4, 10, 16, 22,……….
- Find the sum of the first 20 terms of the arithmetic sequence: 4, 10, 16, 22,……….
- Find the sum of the first 50 terms of the arithmetic sequence: -10, -6, -2, 2,....
- Find the sum of the first 50 terms of the arithmetic sequence: -10, -6, -2, 2,....
- Find 1+2+3+4+...+ 100, the sum of the first 100 natural numbers.
- Find 1+2+3+4+...+ 100, the sum of the first 100 natural numbers.
- Find the sum of the first 60 positive even integers.
- Find the sum of the first 60 positive even integers.
- Find the sum of the even integers between 21 and 45.
- Find the sum of the even integers between 21 and 45.
- Find the sum of the even integers between 21 and 45.
- Find the sum of the odd integers between 30 and 54.
- For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of th...
- For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of th...
- For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of th...
- Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58. Find a14+b12.
- Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58. If {a} is a finite sequence ...
- Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58. Find the difference between ...
- Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58. Find the difference between ...
- In the sequence 21,700, 23,172, 24,644, 26,116,... which term is 314,628?
- Show that the sum of the first n positive odd integers,1 +3 +5 + ··· + (2n − 1), ... is n².
- Use the formula a_n=4+(n-1)(-7) to find the eighth term of the sequence 4, −3, −10,…
- Use the formula a_n=4+(n-1)(-7) to find the eighth term of the sequence 4, −3, −10,…