# The first and the last terms of an AP are 1 and 11. If the sum of its terms is 36, then the number of terms will be:

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The first and the last terms of an AP are 1 and 11. If the sum of its terms is 36, then the number of terms will be:
1. 5
2. 7
3. 6
4. 8

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Correct Answer - Option 3 : 6

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 = 1

Last term of AP = l = 11

Sum of n terms of an AP = 36

⇒ $\rm S_n= \frac{n}{2}×(a+l)$

⇒ 36 = n/2 × (1 + 11)

⇒ 36 = 6n

∴ n = 6