The sum of 13 terms of the series a, 2a, 3a, 4a... is 256. What is a.
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The sum of 13 terms of the series a, 2a, 3a... is 256. This is an arithmetic progression with the first term a and common difference a.
For an arithmetic series with first term a, and common difference d, the sum of the first n terms is (n/2)(2a + (n-1)*d)
The sum of 13 terms of the given series is (13/2)*(2a + 12a)
(13/2)*(2a + 12a) = 256
=> 13*14a = 512
=> a = 256/91
The required value of a = 256/91
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