Quantitative Reasoning

Progression & Series

Medium

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?

✅ Correct Option: 1

The first term $a = 25$ , last term $l = 180$ , and sum $S = 1025$ .

For an arithmetic progression, the sum of all terms is:

$S = \dfrac{n}{2} \times (a + l)$

where $n$ is the number of terms.

Substituting the known values:

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

$1025 = \dfrac{n}{2} \times 205$

$2050 = 205n$

$n = \dfrac{2050}{205}$

$n = 10$

Therefore, there are 10 terms in the arithmetic progression.

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Solution