Fewpal
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If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.

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Sn = 3n2 + 5n

Taking n = 1, we get

S1 = 3(1)2 + 5(1)

⇒ S1 = 3 + 5

⇒ S1 = 8

⇒ a1 = 8

Taking n = 2, we get

S2 = 3(2)2 + 5(2)

⇒ S2 = 12 + 10

⇒ S2 = 22

∴ a2 = S2 – S1 = 22 – 8 = 14

Taking n = 3, we get

S3 = 3(3)2 + 5(3)

⇒ S3 = 27 + 15

⇒ S3 = 42

∴ a3 = S3 – S2 = 42 – 22 = 20

So, a = 8,

d = a2 – a1 = 14 – 8 = 6

Now, we have to find the value of m

an = a + (n – 1)d

⇒ am = 8 + (m – 1)6

⇒ 164 = 8 + 6m – 6

⇒ 164 = 2 + 6m

⇒ 162 = 6m

⇒ m = 27

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