Question

What is the 32nd term of the arithmetic sequence where
a1 = 14 and a13 = -58?

Answer 1

The nth term of an arithmetic sequence is found from:
$n_{th}\ term=a+(n-1)d$
Plugging in the given values, we get for the 13th term:
-58=14+12d
12d =-58 - 14 = -72
d = -6
So, the 32nd term is:
$a_{32}=14+(32-1)-6=-172$