Question

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

Answer 1

Consider the given series.

$[7+\frac{21}{2}+14+...+84]$

$a=7,d=\frac{7}{2},l=84$

Let n be the number of terms,

$l=a+(n-1)d$

$84=7+(n-1)\frac{7}{2}$

$\frac{154}{7}=n-1$

$n=\frac{154}{7}+1$

$n=\frac{161}{7}=23$

Now, the sum of the series,

$S_n=\frac{n(a+l)}{2}$

$S_{23}=\frac{23(7+84)}{2}$

$S_{23}=\frac{23\times 91}{2}=\frac{2093}{2}$

So, the sum of given series is $\frac{2093}{2}.$