Question

write the formula for (a) the nth term and (b)sum of the nth term in an arithmetic progression​

Answer 1

Step-by-step explanation:

The sum of n terms formula is given by,

Sn=2n[2a+(n−1)d] . (1)

Given :- Sn=2n−n2    .. (2)

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

2n(2a+(n−1)d)=2n−n2

2an+n2d−nd=4n−2n2

(2a−d)n+dn2=4n−2n2      3)

On comparing factors of n2 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.