What is the sum of the first 25 terms of an AP whose nth term is given by t = 2 - 3n?

The sum of the first 25 terms of the Arithmetic Progression (AP) is -925.

We are given that the nth term of the AP is defined as t = 2 - 3n. This means a_n = 2 - 3n. To find the sum of the first 25 terms, we can use the formula for the sum of an AP.

Here's how to determine the sum:

1. Find the first term (a₁):
   Substitute n = 1 into the formula for the nth term:
   a₁ = 2 - 3(1) = 2 - 3 = -1

2. Find the 25th term (a₂₅):
   Substitute n = 25 into the formula for the nth term:
   a₂₅ = 2 - 3(25) = 2 - 75 = -73

3. Use the formula for the sum of the first n terms of an AP:
   S_n = n/2 * (a₁ + a_n)

   In this case, n = 25, a₁ = -1, and a₂₅ = -73. Therefore:
   S₂₅ = 25/2 (-1 + (-73))
   S₂₅ = 25/2 (-74)
   S₂₅ = 25 * (-37)
   S₂₅ = -925

Therefore, the sum of the first 25 terms of the AP is -925, as confirmed by the reference provided: "Therefore, sum of first 25 term is −925."