#### 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 a

^{2}− 12 a + 36 = a

^{2}+ 6 a

or

18 a = 36

∴ a = 2

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