Question

To find the sum of the first 24 terms of an AP whose $n^{th}$ term is given by $a_n=3+2n$, what is the best approach to solve this question?

• A. Find the first term and the common difference.
• B. List out the first 24 terms using the expression for n^th term and add them.
• C. Data insufficient - we need the value of “first term” to be given.
• D. Data insufficient - we need the value of “common difference” to be given.

Answer 1

The correct option is A Find the first term and the common difference.

We know that we have two formulae for finding Sum to n terms of an AP.
$S_n=\frac{n}{2}(2a+(n-1\left)d\right)$

where $S_n$ is the sum of n terms of the AP,

'n' is the number of terms of the AP,

'$a$' is the first term of the AP

'd' is the common difference.

Also, $S_n=\frac{n(firstterm+lastterm)}{2}$
Given $a_n=3+2n$

Therefore, $a_1=5,a_2=7,a_3=\mathrm{9.......}{a}_{24}=51$

First term = 5, 24th term = 51, d= 2

Hence, $s_{24}=\frac{24}{2}\left(2\right(5)+23(2\left)\right)$

= 12(56)

= 672