# 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.

9 views

closed
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

by (54.5k points)
selected

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