Question

find the common difference of an AP whose first term is100 and sum of whose first 6 term is 5 times the sum of next 6term

Answer 1

a=100
a+a+d+a+2d+a+3d+a+4d+a+5d=5(a+10d+a+6d+a+7d+a+8d+a+9d+a+11d)
6a+15d=30a+255d
-24a=240d
-24×100/240= -10
so d = -10

Answer 2

first term=100
a+a+d+a+2d+a+3d+a+4d+a+5d=5(a+10d+a+6d+a+7d+a+8d+a+9d+a+11d)
6a+15d=30a+255d
-24a=240d
-24×100/240= -10 
d = -10