SOLUTION: The coefficient of 5th 6th and 7th terms in the expansion ( 1+a)^7 in ascending powers of a forms the arithmetic progressions. Find the A.P

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Question 1014396: The coefficient of 5th 6th and 7th terms in the expansion ( 1+a)^7 in ascending powers of a forms the arithmetic progressions. Find the A.P
Answer by ikleyn(52799) About Me  (Show Source):
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The coefficient of 5th 6th and 7th terms in the expansion ( 1+a)^7 in ascending powers of a forms the arithmetic progressions. Find the A.P
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On binomial expansion see the lesson Binomial Theorem, Binomial Formula, Binomial Coefficients and Binomial Expansion in this site.

7-th term is C%5B7%5D%5E6%2Aa%5E6.

6-th term is C%5B7%5D%5E5%2Aa%5E5.

5-th term is C%5B7%5D%5E4%2Aa%5E4.

C%5B7%5D%5E6 = 7;  C%5B7%5D%5E5 = %287%2A6%29%2F2 = 21;  C%5B7%5D%5E5 = %287%2A6%2A5%29%2F%281%2A2%2A3%29 = 35.

This AP is  35,  21,  7.   Or 7,  21,  35 from the other end.