Given: an = 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.