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An AP has 4 as its first term. what is the common difference if the sum of the first 12...

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user150558 | eNotes Newbie

Posted July 2, 2013 at 4:10 AM via web

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An AP has 4 as its first term. what is the common difference if the sum of the first 12 terms is 2 times the sum of the first 8 terms.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 2, 2013 at 4:19 AM (Answer #1)

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The sum of the first n terms of an AP with first term a and common difference d is equal to `S_n = (n/2)*(2a +(n-1)*d)` .

It is given that the first term of the AP is 4, and the sum of the first 12 terms is 2 times the sum of the first 8 terms.

This gives 6(8 + 11*d) = 2*4*(8 + 7*d)

=> 48 + 66d = 64 + 56d

=> 10d = 16

=> d = 1.6

The common difference of the AP is 1.6

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