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If the sum of n terms of an AP is 3n2 + 5n, then which of its terms is 164?
1. 29th
2. 28th
3. 27th
4. 26th
5.

1 Answer

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Best answer
Correct Answer - Option 3 : 27th

Formula used:

If a and d are the first term and the common difference of AP, then nth term is given by

Tn = a + (n - 1)d

Calculation:

Given that, the sum of n term of AP is 

Sn = 3n2 + 5n       -----(1)

Let a1, a2, a3........an are terms of AP

S1 or a1 = 3(1)2 + 5(1)

a1 = 8      -----(2)

Similarrly,

a1 + a2 = 3(2)2 + 5(2)

⇒ a1 + a2 = 22     ----(3)

a2 = 14

a1 + a2 + a3  = 3(3)2 + 5(3)

⇒ a+ a2 + a3 = 42     ------(4)

a3= 20

Therefore AP is 8, 14, 20.....

Let mth term is 164, then

164 = 8 + (m - 1)6

⇒ m = 27

Hence, option 3 is correct.

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