Question

The sum of the first n terms of an A.P. is 5n − n2

. Find the nth term of this A.P.​

Answer 1

Sn=5n-n2

S(n-1)=5(n-1)-(n-1)2

=5n-5-n2-1+2n

=7n-6-n2

Therefore Tn = S(n) - S(n-1)

=5n-n2-7n+6+n2

= -2n+6

= 6-2n=2(3-n)..... (ans)

(tips, just put nos in these places to understand the concept more clearly).

Just remember this

Note: S2=T1+T2

S3=T1+T2+T3

THEN, S3-S2 = T1 +T2+T3-T1-T2 = T3.