The sum of four numbers in gp is 60

Asked by admin @ 20/08/2021 in Math viewed by 323 People

The sum of four numbers in GP is 60 and the a.m. of the first and the last is 18 the numbers are

Answered by admin @ 20/08/2021

Answer:

Let the four terms of Gp be $a,ar,ar^2,ar^3$

The sum of four numbers in GP is 60

So, $a+ar+ar^2+ar^3=60$ ---A

We are given that the a.m. of the first and the last is 18

So, $\frac{a+ar^3}{2}=18$

$a+ar^3=36$ --B

Substitute the value in A

$36+ar+ar^2=60$

$ar+ar^2=60-36=24$ ---C

Divide B and C

$\frac{a+ar^3}{ar+ar^2}=\frac{36}{24}$

$\frac{1+r^3}{r+r^2}=\frac{36}{24}$

$2r^3-3r^2-3r+2=0$

$r=-1,\frac{1}{2},2$

So, at r = 1/2

$a(1+\frac{1}{2}^3)=36$

$a=32$

$a,ar,ar^2,ar^3=32,16,8,4$

At r = 2

$a(1+2^3)=36$

$a=2$

$a,ar,ar^2,ar^3=32,64,128,256$

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