Question

Find the sums given below:
7 + 10$\frac{1}{2}$ + 14 +......+84

• A. 1066$\frac{1}{2}$
• B. 1096$\frac{1}{2}$
• C. 1046$\frac{1}{2}$
• D. 1006$\frac{1}{2}$

Answer 1

The correct option is C 1046$\frac{1}{2}$

In given series of AP first term a=7, common difference d= $10\frac{1}{2}-7=\frac{21}{2}-7=\frac{7}{2}$ and last term l=84
Since, $l=a+(n-1)d$
$\Rightarrow 84=7+(n-1)\frac{7}{2}$
$\Rightarrow 84-7=(n-1)\frac{7}{2}$
$\Rightarrow 77=(n-1)\frac{7}{2}$
$\Rightarrow 77\times \frac{2}{7}=n-1$
$\Rightarrow 22=n-1$
$\Rightarrow n=23$
Since, $S_n=\frac{n}{2}(a+l)$
$\Rightarrow S_n=\frac{23}{2}(7+84)$
$\Rightarrow S_n=91\times \frac{23}{2}$
$\Rightarrow S_n=\frac{2093}{2}$
$\Rightarrow S_n=1046\frac{1}{2}$