The sum of 13 terms of the series a, 2a, 3a, 4a... is 256. What is a.
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