Question

Solve the following equations $1+6+11+16+........+x=148$

Answer 1

Given,

$a=1$

$d=6-1=5$

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]=148$

$148\times 2=n\left[2\right(1)+(n-1\left)\right(5\left)\right]$

$296=n[2+5n-5]$

$5n^2-3n-296=0$

$(n-8)(n+\frac{37}{5})=0$

$\therefore n=8$

$S_n=\frac{n}{2}[a+x]$

$148=\frac{8}{2}[1+x]$

$37=1+x$

$\therefore x=36$