Question

Find the common difference of an ap whose first trem is 100 and sum of whose firts 6 terms is 5 times the sum of next 6 terms

Answer 1

Let AP be a, a+d, .. where a = 100, d= d

Sn= a + (n-1)d

100 + 5d

Next 6 terms are

a+6d, a+ 7d.............a+ 11d

Sn = a+ 6d + ( a + 6d+ a+ 11d)

=2a+ 23 d

100+ 5d = 5( 2a+ 23d)

100 + 5 d = 1000+ 23 d

900 = - 18 d

d = -50