Question

Sum of $1ton$ natural number is $36$ then find the value of $n$.

Answer 1

$a=1,d=1$

$S_n=36$

$\frac{n}{2}[2a+(n-1\left)d\right]=36$

$\frac{n}{2}[2+(n-1\left)\right]=36$

$n[2+(n-1\left)\right]=72$

$n[n+1]=72$

$n^2+n-72=0$

$n^2+9n-8n-72=0$

$(n-8)(n+9)=0$

$\therefore n\ne 9,n=8$