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If the sum of n terms of an AP is 300, first terms is 10 and last term is 50 then n is equal to ?
1. 6
2. 8
3. 9
4. 10
5. None of these

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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

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