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
The sum of an arithmetic progression is the number of terms times the average of the first and last terms: \(\displaystyle S=\frac{n}{2}(a+l)\).
\(\displaystyle 1025=\frac{n}{2}(25+180)=\frac{n}{2}\times205\)
\(\displaystyle n=\frac{2\times1025}{205}=10\)