Question

Iv)

The sum of
four numbers in G.P. is 80 and the A.M. between the
first and the last is 28. Show that the numbers are 2, 6, 18, 54.
​

Answer 1

Explanation:

Given numbers : 2 , 6, 18, 54

Since common ration between numbers,

`common \ ratio \ in \ GP , \ r = (a_n)/(a_(n-1)) = (6)/(2) = 3`

So the numbers are in GP.

Now Sum of the numbers = 2 + 6 + 18 + 54 = 80

AM, arithmetic mean between first and last number :

`(54+2)/(2) = (56)/(2) =28`

All the conditions are true.