Question

What is the 32nd term of the arithmetic sequence where a1 = 13 and a13 = –59?

Answer 1

the term in an arithmetic sequence is

\[T _{n}=a + (n -1)d\]

us the information for the 13th term to find the common difference

\[-59 = 13 + (13 -1 )d\]

you need to solve

-59 = 14 + 12d

then with your value of d, a = 13 and n = 31, find the 32nd term by using the equation above.