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 a_{1} + a_{2} + ....... a_{6} =5 (a_{7} + ........ + a_{12})
6( a1 + a6/2) = 5 x 6 (a_{7} +a_{12}/2)
⇒ a + a + 5d = 5[a + 6d + a + 11d]
⇒ 8a + 80d = 0 (a = 100)
⇒ d = - 10.