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Question
Find the sum of the following arithmetic series:
34 + 32 + 30 +...+10
Solution
The given arithmetic series is 34 + 32 + 30 +.....+10.
Here, a = 34,d = 32-34 = -2 and l = 10.
Let the given series contain n terms. Then,
an = 10
⇒ 34 + (n-1) × (-2) = 10 [an = a+ (n-1) d]
⇒ - 2n + 36 = 10
⇒ -2n = 10-36=-26
⇒ n= 13
∴ Required sum` 13/2 xx (34+10) [ s_n = n/2 ( a+l)]`
= `13/2 xx 44 `
= 286
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