Sum of 1 to n natural numbers is 36, then find the value of n.

Answer

The value of `n` is 8.

Explanation

Here, `S_(n)=36,a=1`, the difference between consecutive natural numbers `=d=1`
`S_(n)=(n)/(2)[2a+(n-1)d]` …(Formula)
`therefore36=(n)/(2)[2xx1+(n-1)1]`
`therefore36xx2=n(2+n-1)`
`therefore72=n(n-1)`
`thereforen(n+1)=72`
`thereforen^(2)+n-72=0`
`thereforen^(2)+9n-8n-72=0`
`thereforen(n+9)-8(n+9)=0`
`therefore(n+9)(n-8)=0`
`thereforen+9=0orn-8=0`
`thereforen=-9 orn=8`.
But the nautral cannot be negative
`thereforen=-9` is unacceptable.
`thereforen=8`