Question

the sum of first n terms of an a.p. is given by Sn= 7nsquare-3n. find the nth Term of a.p.

Answer 1

hi, frnd
here is your answer
sn = 7n^2-3n
now substituting n=1 we get the first term
a = 7-3 = 4
sn = n/2(an+a)
here sn is the sum of n terms, an-last term
,a-first term.
so 7n^2-3n = n/2(an+4)
2(7n-3) = an+4
an = 14n-6-4 = 14n-10
hence the nth term of the a. p is
an = 14n-10

Answer 2

Given:Sum of n terms-Sn=7n²-3n

nTH term= Sum of (n)terms - S(n-1)terms →[1]

Acc. to que.
→S(n-1)=7(n-1)²-3(n-1)
→S(n-1)=7(n²-2n+1) - 3n - 3
→S(n-1)=7n²-14n+7-3n-3

→S(n-1)=7n²-17n+10 →[2]

Again Given: Sn=7n²-3n
Equating this with [1] and [2]

We get:
nTH term = 7n²-3n - ( 7n²-17n+10)
→nTH term= 7n²-3n-7n²+17n-10
→nTH term=7n²-7n² +17n-3n -10
→nTH term=14n-10

So To Conclude:: nTH term we require is [14n-10]

Hope it helps...

if it is wrong... kindly ignore
Good Luck.