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in Arithmetic Progression by (30.9k points)
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If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164? 

A. 26th 

B. 27th 

C. 28th 

D. none of these

1 Answer

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by (31.3k points)
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Best answer

Here, Sn = 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.

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