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# Find the Sum of the First 11 Terms of the A.P : 2, 6, 10, 14, ... - CBSE Class 10 - Mathematics

ConceptSum of First n Terms of an AP

#### Question

Find the sum of the first 11 terms of the A.P : 2, 6, 10, 14, ...

#### Solution

In the given problem, we need to find the sum of terms for different arithmetic progressions. So, here we use the following formula for the sum of n terms of an A.P.,

S_n = n/2[2a  + (n - 1)d]

Where; a = first term for the given A.P.

d = common difference of the given A.P.

= number of terms

2, 6, 10, 14, ... to 11 terms

Common difference of the A.P. (d) = a_2 - a_1

= 6 - 2

= 4

Number of terms (n) = 11

The first term for the given A.P. (a) = 2

So, using the formula we get,

S_n = 11/2 [2(2) + (11 - 1)(4)]

= (11/2)[4 + (10)(4)]

= (11/2)[4 + 40]

= (11/2) [44]

= 242

Therefore, the sum of first 11 terms for the given A.P. is 242

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Solution Find the Sum of the First 11 Terms of the A.P : 2, 6, 10, 14, ... Concept: Sum of First n Terms of an AP.
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