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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.
n = 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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