find the common difference of an ap whose first

Question

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.