Question :

In a set of four numbers the first three are in G . P . and the last three in A . P . with common difference 6 . If the first number is the same as the fourth, find the four numbers.
Submitted on 8/7/2024 | Answered by Vandana Rana

Answer :

Last three of the four numbers are in A . P.
Let them 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

a2−12a+36=a2+6a
or
18a=36

∴a=2

The four numbers are 8, -4, 2, 8, which satisfy the given conditions.