Question

The first term of an AP is 25; sum of the first n terms being 60 and nth term is −17. Find the tenth

term.

Answer 1

first term = 25

sum of first n terms = 60
Sn = 60 ,

use formula,
Sn =n/2{first term + nth term }

60 =n/2{ 25 -17}

120 = n(8)

n= 15

hence, Tn = -17
use formula,
Tn = a + (n -1)d
-17 = 25 + (15-1)d
-42 = 14d

d = -3

so, 10th term = 25 + (10-1)(-3)
= 25 -27 = -2

Answer 2

Nice question.
Answer explained below.
Comment below if any doubt occurs to you.