Question

If sum of n terms of A.P. is 3n²/2 + 5n/2 then find its 25^th term.

Answer 1

Let the sum of n terms be given by S_n

So

S_n = \(\frac{3n^2}{2} + \frac{5n}2\)

S₁ = \(\frac{3(1)^2}{2} + \frac{5(1)}2\)

= \(\frac{3}{2} + \frac{5}2\)

= 4

So 1st term is 4 say ′a′

Now

S₂ = \(\frac{3(2)^2}{2} + \frac{5(2)}2\)

= 6 + 5

= 11

Now a₂ = S₂ − a₁

⇒ a₂ = 11 − 4 = 7

Now common difference (d)

= a₂ − a₁

= 7 − 4

= 3

We know , n th term of A.P. is given as,

a_n = a + (n−1)d

So,

a₂₅ = 4 + (25 − 1)(3)

⇒ a₂₅ = 4 + 24 × 3

= 4 + 72

Hence, 25th term of the AP is 76.

Answer 2

Given that, sum of n terms of A.P.

S_n = 3n²/2 + 5n/2

Hence 25^th term will be 76.