Question

find the sum given below
$7+10\frac{1}{2}+14+....+84$

Answer 1

It is an AP with $a=7$ & $d=3\frac{1}{2}=\frac{7}{2}$

$l_n=a+(n-1)d=84$ [ To find $n$]

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

$\Rightarrow (n-1)\frac{7}{2}=77\Rightarrow (n-1)=22$

$\Rightarrow n=23$

$Sn=\frac{n}{2}[a+l]$

$Sn=\frac{23}{2}[7+84]$

$Sn=\frac{2093}{2}=1046\frac{1}{2}$