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
We are asked to find the sum of 24 terms of the sequence:
$a_n = 3 + 2n$
Step 1: First term ($a_1$) and 24th term ($a_{24}$)
$a_1 = 3 + 2(1) = 5$
$a_{24} = 3 + 2(24) = 3 + 48 = 51$
Step 2: Sum of first n terms of an arithmetic progression
Formula:
$S_n = \frac{n}{2} (a_1 + a_n)$
$S_{24} = \frac{24}{2} (5 + 51) = 12 \times 56 = 672$