9. Sequences, Series, & Induction

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.

${\sum }_{i=1}^{100}4i$

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

Write a recursive formula for the arithmetic sequence.

$\(\left\]\lbrace\)8,2,-4,-10,\(\ldots\[\right\]\rbrace\)$

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

Write the first six terms of each arithmetic sequence. a_n = a_n-1 -10, a₁ = 30

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_n} and the sum of the first 14 terms of {a_n}.

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 a_n to find a₂₀, the 20th term of the sequence. -7, -3, 1, 5 ...

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

${\sum }_{i=1}^{16}(3i+2)$

Write the first six terms of each arithmetic sequence. a_n = a_n-1 -0.4, a₁ = 1.6

Write the first six terms of each arithmetic sequence. a₁ = 200, d = 20

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

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

Write the first six terms of each arithmetic sequence. a_n = a_n-1 +6, a₁ = −9