Question

In a certain A.P. the 32nd term is twice the 12th term. Prove that 70th term is twice the 31st term.

Answer 1

a+31*d=2(a+11*d)
TO PROVE : a+69*d=2(a+30*d)
proof:
a+31*d=2(a+11*d)
a+31*d=2*a+22*d 
2*a-a   =31*d-22*d
a          =9*d
put a=9*d in R-H-S OF TO PROVE i.e.2(a+30*d)
=2(9*d+30*d)
=2(39*d)
=78*d
also solve L-H-S separately of TO PROVE i.e.a+69*d put a=9*d
=9*d+69*d
=78*d
since, L-H-S=R-H-S,
HENCE PROVED THAT
a+69*d=2(a+30*d)

Answer 2

70th term of ap is twice the 31st term hence proved....