Sum

Determine the sum of first 100 terms of given A.P. 12, 14, 16, 18, 20, ......

Activity :- Here, a = 12, d = `square`, n = 100, S_{100} = ?

S_{n} = `"n"/2 [square + ("n" - 1)"d"]`

S_{100} = `square/2 [24 + (100 - 1)"d"]`

= `50(24 + square)`

= `square`

= `square`

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#### Solution

Here, a = 12, d = 14 - 12 = **2**, n = 100, S_{100} = ?

S_{n} = `"n"/2 [2"a" + ("n" - 1)"d"]`

S_{100} = `100/2 [24 + (100 - 1)"d"]`

= 50[24 + 99(2)]

= 50(24 + **198**)

= **50(222)**

= **11100**

Concept: Sum of First n Terms of an AP

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