The sum of first n terms of an A.P. is $3 n^{2}$ +4n. Find the 25th term of this A.P.

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Solution

Given S_n = 3n² + 4n

S₁ = 3×1 + 4×1 = 7.

S₂ = 3×4 + 4×2 = 12 + 8 = 20.

Therfore First term a₁ = 7 & Second term a₂ = 20 - 7 = 13 and d = 13 - 7 = 6.

Now 25^th term a_n= 7 + ( 25 - 1) 6

a₂₅ = 7 + 24 x 6

a₂₅ = 151.

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