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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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