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?
Answer & explanation
Correct answer: option 1
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
$n = \frac{1025}{102.5} = 10$