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 − 12 a + 36 = a2 + 6 a
or
18 a = 36
∴ a = 2
. the four numbers are 8 , − 4 , 2 , 8 , which satisfy the given conditions