Q. 54.4( 8 Votes )

# If the sum of n terms of an A.P. is 3n^{2} + 5n then which of its terms is 164?

A. 26^{th}

B. 27^{th}

C. 28^{th}

D. none of these

Answer :

Here, S_{n} = 3n^{2} + 5n

S_{1} = a_{1} = 3 + 5 = 8

S_{2} = a_{1} + a_{2} = 12 + 10 = 22

⇒ a_{2} = S_{2} – S_{1} = 22 – 8 = 14

S_{3} = a_{1} + a_{2} + a_{3} = 27 + 15 = 42

⇒a3 = S3 – S2 = 42 – 22 = 20

∴ Given AP is 8, 14, 20, .....

Thus a = 8, d = 6

Given t_{m} = 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.

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