Question

If the third and ${11}^{th}$ term of an A.P are $8$ and $20$ respectively, find the sum of first ten terms.

• A. $105\frac{1}{2}$
• B. $108$
• C. $117\frac{1}{2}$
• D. $203\frac{1}{2}$

Answer 1

The correct option is C $117\frac{1}{2}$

As we know nth term, $a_n=a+(n-1)d$

& Sum of first $n$ terms, $S_n=\frac{n}{2}(2a+(n-1\left)d\right)$, where $a$ & $d$ are the first term & common difference of an AP.

Since, $a_3=a+2d=8$ ------(1)

$a_{11}=a+10d=20$ -----(2)

By solving above two equations, we get $a=5,d=\frac{3}{2}$
$\therefore S_{10}=\frac{10}{2}[2a+(10-1)d]$
$=5[2\times 5+9\times \frac{3}{2}]$
$=117\frac{1}{2}$