Posted by **Dhanalakshmi** on Wednesday, March 16, 2011 at 8:58am.

In Geometric progression the sum of first of three terms is 28 and the product is 512 find those numbers

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**bobpursley**, Wednesday, March 16, 2011 at 9:18am
a+ar+ar^2=28

a^3 * r^3=512

one the second equation, take the cube root of each side.

ar=cubrt(512)=8

a+8+ar^2=28

a(1+r^2)=20

but a= 8/r

8(1+r^2)=20r

8r^2-20 r+8=0

r=(20)+-sqrt(400-256) /16

r=20+- sqrt(144) /16 = (20+-12)/16=2 or 1/2

then a= 4 or 16

check a=4, r=2

4 + 8 + 16=28

a^3 r^3=64*8=512 checks, a=4, r=2

check a=8, r=1/2

8 +4 + 2 does not check.

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