Correct Answer - Option 3 : 27
th
Formula used:
If a and d are the first term and the common difference of AP, then nth term is given by
Tn = a + (n - 1)d
Calculation:
Given that, the sum of n term of AP is
Sn = 3n2 + 5n -----(1)
Let a1, a2, a3........an are terms of AP
S1 or a1 = 3(1)2 + 5(1)
⇒ a1 = 8 -----(2)
Similarrly,
a1 + a2 = 3(2)2 + 5(2)
⇒ a1 + a2 = 22 ----(3)
⇒ a2 = 14
a1 + a2 + a3 = 3(3)2 + 5(3)
⇒ a1 + a2 + a3 = 42 ------(4)
⇒ a3= 20
Therefore AP is 8, 14, 20.....
Let mth term is 164, then
164 = 8 + (m - 1)6
⇒ m = 27
Hence, option 3 is correct.