Question

If the sum of n terms of an AP is 3n^2 + 5n then which of its terms is 164

Answer 1

Sn = 3n²+5n

S1 =a1 = 8

so 1st term is 8

now S2 -S1 = a2

so

a2 = 22-8

a2 = 14

now d = a2-a1

so d = 6

now An = a+(n-1)d

plug the values simply

164 = 8 + (n-1)6

156/6 = n-1

162/6 = n

=> n = 27