Question

Find four numbers in G.P.such that their product is I and the sum of the middle two 10 numbers 1S

Answer 1

Answer:

Last three of the four numbers are in A.P. and hence they may be chosen as a−d,a,a+d

Also the first number is same as the last one i.e. a+d.

Therefore the four numbers are a+d,a−d,a,a+d. The first three of the above four are in G.P.

∴(a−d)

2

=a(a+d). But d=6 given

∴(a−6)

2

=a(a+6)

or a

2

−12a+36=a

2

+6a

or 18a=36 ∴a=2.

Putting for a and d the four numbers are 8,−4,2,8, which satisfy the given conditions.