**Question:**

If, for a positive integer $n$, the quadratic equation,

$$

x(x+1)+(x+1)(x+2)+\ldots . .+(x+\overline{n-1})(x+n)=10 n

$$

has two consecutive integral solutions, then $n$ is equal to:

Correct Option: 1

JEE Main Previous Year 2017

**Solution:**

If, for a positive integer $n$, the quadratic equation,

$$

x(x+1)+(x+1)(x+2)+\ldots . .+(x+\overline{n-1})(x+n)=10 n

$$

has two consecutive integral solutions, then $n$ is equal to:

Correct Option: 1

JEE Main Previous Year 2017
**Solution:**