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If the sum of n terms of an AP is 450, first terms is 15 and last term is 60 then find the value of n.
1. 8
2. 20
3. 12
4. 14

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Correct Answer - Option 3 : 12

Concept:

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

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

Where l is the last term of the AP

Calculation:

Given: First term of AP = a = 15

Last term of AP = l = 60

Sum of n terms of an AP = 450

⇒ \(\rm S_n= \frac{n}{2}×(a+l)\)

⇒ 450 = n/2 × (15 + 60)

⇒ 6 = n/2

∴ n = 12

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