Question

the sum of first n terms of an AP is given by 5n2+3n. If its nth term is 168, find n. Also find 20th term of the AP.

Answer 1

If the sum of first n terms is 5n^2+3n,

Then it's first term is =5x1x1+3x1
=8

Sum of two terms will be=5x2x2+3x2
=46

So, second term=46-8
=38

Therefore d=38-8 = 30

Now, sum of n terms =n/2(2a+(n-1)d)
5n^2+3n. = n/2(2x8+(n-1)x30)
5n^2+3n. = n/2(16+(n-1)30)
10n^2+16n=30n^2-14n
20n. =20n^2

n=1

20th term of AP = 578