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Question
Find the sum of the following arithmetic progressions:
−26, −24, −22, …. to 36 terms
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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
−26, −24, −22, …. to 36 terms
Common difference of the A.P. (d) = `a_2 - a_1`
= (-24) - (-26)
= - 24 + 26
= 2
Number of terms (n) = 36
The first term for the given A.P. (a) = −26
So, using the formula we get,
`S_36 = 36/2 [2(-26) + (36 - 1)(2)]`
= (18)[-52 + (35) (2)]
= (18)[-52 + 70]
= (18)[18]
= 324
Therefore the sum of first 36 terms for the given A.P is 324
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