Question

in an ap sum of first n terms is n^2+2n.find its 18th term

Answer 1

sum = n^2 + 2n
sum of 1 term = S1 = 1^2 + 2×1 = 3 = a1
sum of 2 terms = S2 = 2^2 + 2×2 = 8
a1 + a2 = S2 = 8
a2 = 8 - 3 = 5
d = a2 - a1 = 5 - 3 = 2
a18 = a1 + (18 - 1)d
a18 = 3 + 17 × 2 = 37
18th term is 37

Answer 2

let n=1 so
n^2+2n=(1)^2+2(1)
1+2=3
n=3
2^2+2×2=4+4
8
n=3
3^2+3×2
=9+6=15
3,8,15......Sn
3,5,7.........An
a18=a+17d
3+17(2)
3+34
=37