Question

in an AP if Sn = 3n^2 + 5n and k term = 164 find the value of k

Answer 1

S(K)=3K^2+5K
S(K-1)=3(K-1)^2+5(K-1)
S(K)-S(K-1)=Kth term
6K+2=164
6K=162
K=27

Answer 2

Hello there
The the of first n terms of the AP is
Sn=3n²+5n
and,the sum of first n-1 terms will be
S(n-1)=3(n-1)²+5(n-1)
=3(n²-2n+1)+5(n-1)
=3n²-n-2
Now difference of Sn and S(n-1) will give us the nth term An.
An=Sn-S(n-1)=(3n²+5n)-(3n²-n-2)=6n+2
now,An=6n+2
so,Ak=6k+2=164
or,6k=162
or,k=162/6=27
Answer.