Find the common difference of an ap, Mathematics

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Find the common difference of an AP whose first term is 100 and sum of whose first 6 terms is 5 times the sum of next 6 terms.

Ans:    a = 100

APQ a1 + a2 + ....... a6 =5 (a7 + ........ + a12)

6( a1 + a6/2) = 5 x 6 (a7 +a12/2)

 

⇒ a + a + 5d = 5[a + 6d + a + 11d]

⇒ 8a + 80d = 0 (a = 100)

⇒ d = - 10.

 

 


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