Find the sum of first 25 terms of an A.P. whose nth term is 1 — 4n.

Given: a_n = 1 – 4n

Taking n = 1,

a₁ = 1 – 4(1) = 1 – 4 = -3

Taking n = 2,

a₂ = 1 – 4(2) = 1 – 8 = -7

Taking n = 3,

a₃ = 1 – 4(3) = 1 – 12 = -11

Therefore the series is -3, -7, -11, …

So, a = -3, d = a₂ – a₁ = -7 – (-3) = -7 + 3 = -4

Now, we have to find the sum of the first 25 terms of the AP

⇒ S₂₅ = 25 × (-51)

⇒ S₂₅ = -1275

Hence, the sum of 25 terms is -1275.