Question 8
The sum of first n terms of an AP is given by Sn = 2n2 + 3n . Find the sixteenth term of the AP.
Given
Sn = 2n2 + 3n
Taking n = 1
S1 = 2 12 + 3 1
= 2 + 3
= 5
So, Sum of first term of AP is 5
But sum of first term will be the first term
So, First term = a = 5
Taking n = 2 in Sn
S1 = 2 22 + 3 2
S2 = 2 4 + 6
S2 = 8 + 6
S2 = 14
Sum of first 2 terms is 14
Finding 2nd term
Sum of first 2 terms is 14
First term + Second term = 14
5 + a2 = 14
a2 = 14 5
a2 = 9
Hence in AP ,
First term = a = 3
Common difference = d = Second term First term
= 9 5
= 4
We need to find 16th term
We know that
an = a + (n 1) d
a16 = a + (16 1) d
= a + 15d
= 5 + 15 4
= 5 + 60
= 65

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.