Question

for the series Sn=n^2 obtain the formula of corresponding sequences​

Answer 1

The sum of n terms formula is given by,

S n = 2n

[2a+(n−1)d] ........... (1)

Given :- Sn =2n−n 2

......... (2)

Comparing equation (1) & (2), we get

2n

(2a+(n−1)d)=2n−n 2

2an+n

2 d−nd=4n−2n

2

(2a−d)n+dn

2

=4n−2n

2

.......... (3)

On comparing factors of n

2 in equation (3)

d=−2

On comparing factors of n in equation (3), we have

2a−d=4

2a=4+d

2a=4−2

2a=2

a=1

Therefore, the first term, a=1 and the common difference, d=−2.