The first and the last terms of an arithmetic progression are 25 and 180, respectively. If the sum of all the terms is 1025, how many terms are there?

10

The correct answer is Option (1) → 10

Step 1: Recall the formula for the sum of an AP

$S_n = \frac{n}{2} \left(a + l\right)$

Where:

• $S_n$​ = sum of n terms
• a = first term = 25
• l = last term = 180
• n = number of terms

Given $S_n = 1025$

Step 2: Substitute values

$1025 = \frac{n}{2} (25 + 180)$

$1025 = \frac{n}{2} \cdot 205$

$1025 = 102.5 \cdot n$

Step 3: Solve for n

$n = \frac{1025}{102.5} = 10$