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Question
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"]`
S100 = `square/2 [24 + (100 - 1)"d"]`
= `50(24 + square)`
= `square`
= `square`
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Solution
Here, a = 12, d = 14 – 12 = \[\boxed{2}\], n = 100, S100 = ?
Sn = \[\frac{\text{n}}{2} [\boxed{\text{2a}} + (\text{n} - 1)\text{d}]\]
S100 = \[\frac{\boxed{100}}{2} [24 + (100 - 1)\text{d}]\]
= 50[24 + 99(2)]
= \[50(24 + \boxed{198})\]
= \[\boxed{50(222)}\]
= \[\boxed{11100}\]
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