9. Sequences, Series, & Induction

Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a₆₀ when a₁ = 35, d = -3.

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

Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58. If {a_n} is a finite sequence whose last term is -83, how many terms does {a_n} contain?

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

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

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.

${\sum }_{i=1}^{17}(5i+3)$

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

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

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. a_n= a_n-1 -10, a₁ = 30

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

Write the first six terms of each arithmetic sequence. a₁= 5/2, d = -1/2

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\)$

Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a₅₀ when a₁ = 7, d = 5.