**Solution:** We have given

S = 3n^{2} + 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.**