Question

Find the sum of $35$ terms of the series whose $p^{th}$ term is $\frac{p}{7}+2$.

Answer 1

$T_P=\frac{P}{7}+2$
Sum $=\sum _{P=1}^{35}(\frac{P}{7}+2)$
$=\frac{1}{7}{\sum }_{P=1}^{35}P+2{\sum }_{P=1}^{35}\left(1\right)$
$=\frac{1}{7}[1+2+3+4+..........+35]+2[1+1+1+1+..........35terms]$
$=\frac{1}{7}\times \frac{35\times (35+1)}{2}+2\times 35$
$=5\times 18+70$
$=90+70$
$=160$