Question

If the sum of n terms of an A.P. is 3n^2 + 5n and its mth term is 164, find the value of m.

Answer 1

Solution: We have given

S = 3n² + 5n

S1 = a1 = 3 + 5 = 8

S2 = a1 + a2 = 12 + 10 = 22          

 ⇒ a2 = S2 - S1 = 22 - 8 =  14

S3 = a1 + a2 + a3  = 27 + 15 = 42

⇒a3 = S3 - S2 =  42 - 22 = 20

∴ Given AP is 8,14,20,.....

Thus a = 8 , d = 6         

Given tm = 164.

164 =  [a + (n -1)d]

164 =  [(8) + (m -1)6]

164 = [8 + 6m - 6]

164 = [2 + 6m]

162= 6m

m = 162 / 6.

∴ m = 27.