Question

if the sum of first n terms of an A. P.is n²,find the 5th term of the A.P.

Answer 1

given Sn = n²
we know ,
Tn = Sn - S(n -1)
= n² - (n -1)²
=n² -n² +2n -1
=2n -1

hence , Tn = 2n -1

now , 5th term = T5 = (2×5-1) = 10-1 =9

Answer 2

sum of 1st term ,
n=1.
it is given n^2
thus first term = 1 * 1 = 1

sum of two terms,
n=2
=2*2 = 4
2nd term = sum of first 2 term - first term
=4-1 = 3

now we found the AP,
1,3,5,7............

where a= 1
 d= 3 - 1=2

5th term = a+4d
a5 = 1 + 4 * 2
a 5 = 1 + 8
thus 5th term = 9//


hope it helps!!!