10. Sequences, Induction, and Probability

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

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.

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

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 ...

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,...

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,...

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.

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

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

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 even integers between 21 and 45.

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.

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.

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}.

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

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

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.

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 use a recursion formula. Then use the formula for to find the 20th term of the sequence. a1=-20, d = -4

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

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.

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?

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

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

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

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 use a recursion formula. Then use the formula for to find the 20th term of the sequence. a1 = 9, d=2

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

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 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 the first n terms of an arithmetic sequence to find the indicated sum.

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

Find a14+b12.

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

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. an = an-1 -10, a₁ = 30

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.

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 use a recursion formula. Then use the formula for to find the 20th term of the sequence. a1 = 9, d=2

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

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

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.