Correct Answer - Option 4 : 10

__Concept__**:**

The sum of n terms of an AP with first term a and common difference d is given by:

\(\rm {S_n} = \frac{n}{2} × \left[ {2a + \left( {n - 1} \right)d} \right]\;or\;{S_n} = \frac{n}{2} × \left[ {a + l} \right]\)

Where l is the last term of the AP.

**Calculation:**

Given: First term of AP = a = 10

Last term of AP = l = 50

Sum of n terms of an AP = 300

As we know, sum of n terms of an AP = \(\rm {S_n} = \frac{n}{2} × \left[ {a + l} \right]\)

⇒ 300 = \(\rm \frac n 2\) (10 + 50)

⇒ 300 = \(\rm \frac n 2\) × 60

⇒ 5 = \(\rm \frac n 2\)

∴ n = 10