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

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timw996 | Student, Grade 10 | (Level 1) Salutatorian

Posted September 6, 2013 at 2:33 PM via web

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

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 6, 2013 at 2:37 PM (Answer #1)

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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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