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प्रश्न
Find the sum of the following arithmetic progressions:
−26, −24, −22, …. to 36 terms
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उत्तर
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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Q.7
Determine the sum of first 100 terms of given A.P. 12, 14, 16, 18, 20, ......
Activity :- Here, a = 12, d = `square`, n = 100, S100 = ?
Sn = `"n"/2 [square + ("n" - 1)"d"]`
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= `50(24 + square)`
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= `square`
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