Question

What is the 35th term of the arithmetic sequence where a_1 = 13 and a_17 = -35
a. -89

b. -86

c. -83

d. -80

Answer 1

well you need to find the common difference

the formula for a term in an arithmetic sequence is

\[a_{n} = a_{1} + (n - 1)d\]

so to find d, you know

\[a_{1} = 13 ~~and ~~n = 17\]

substitute and then solve for d.

Answer 2

so after you have found d, you can find the 35th term using

\[a_{1} = 13~~~and~~~n = 35\]