Question

if sn, the sum of n term of an AP ,is given by sn=5n^2+3n then find its nth term

Answer 1

sn = 5n^2 + 3n

so if we put n=1 we get the sum of first term it means sum of only one term so we get first term

a1 = 5(1)^2 + 3(1)
a1 = 5 + 3
a1 = 8

now put n=2
we get sum of first two terms
that is
a1 + a2 = 5(2)^2 + 3(2)
a1 + a2 = 5(4) + 6
a1 + a2 = 20 + 6
a1 + a2 = 26
8 + a2 = 26. (since a1 = 8)
a2 = 26 - 8
a2 = 18

so for common difference
d = a2 - a1
d = 18 - 8
d = 10

so nth term will be

an = a + (n-1)d
an = 8 + (n-1)10
an = 8 + 10n - 10
an = 10n -2