Question

if the nth term of an A.P.(2n+1),find the sum of first n terms the AP.

Answer 1

the nth term of an AP = an = (2n+1)
therefore the first term = (2*1+1) = 3
second term = (2*2+1) = 5
d = t2-t1 = 5-3 = 2
so the AP is 3, 5, 7, ....
Sn = (2a+(n-1)d)n/2 = (6+(n-1)2)n/2 = (6+2n-2)n/2
= (4+2n)n/2 = (2+n)n
therefore sum of first n terms is given by (2+n)n