Question

The sum of first n terms of an AP is 3n² + 4n. Find the 25^th term of this AP ?

Answer 1

The sum of first n terms (S_n) is given as `S_n=3n^2+4n`.

So, first term (a₁) =`S_n=3(1)^2+4(1)=7`

`S_2=a_1+a_2=3(2)^2+4(1)=7`

a₂ = 20 − a₁ = 20 − 7 = 13

So, common difference (d) = a₂− a₁ = 13 − 7 = 6

∴n^th term is given by, a_n = a + (n − 1) d

Thus, 25^th term = a₂₅ = 7 + (25 − 1) × 6 = 7 + 24 × 6 = 7 + 144 = 151