Find the sum of 24 terms of the list of numbers whose nth term is given by:
\(a_n=3+2n\)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 672
The \(n\)th term \(3+2n\) grows by 2 each time \(n\) goes up by 1, so the numbers form an arithmetic progression (AP). The sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}(\text{first term}+\text{last term})\).
First term \(a_1=3+2\times1=5\)
24th term \(a_{24}=3+2\times24=51\)
\(\displaystyle S_{24}=\frac{24}{2}(5+51)=12\times56=672\)