Question

The sum of three consecutive terms of a geometric progression is 42, and their product is 512. Find the three terms.

Answer 1

use your definitions:
"The sum of three consecutive terms of a geometric progression is 42"
----> a + ar + ar^2 = 42
a(1 + r + r^2) = 42 **

"their product is 512" --- a(ar)(ar)^2 = 512
a^3 r^3 = 512
(ar)^3 = 8^3
ar = 8 ***

divide ** by ***
(1+r + r^2)/r = 42/8 = 21/4
4r^2 + 4r + 4 = 21r
4r^2 - 17r + 4 = 0
(4r - 1)(r - 4) = 0
r = 1/4 or r = 4

if r = 4, in ar= 8 , a = 2
the 3 terms are 2, 8, and 32
check: sum = 2+8+32 = 42 ⩗
product = 2 x 8 x 32 = 512 ⩗

I will leave it up to you to find the other case.

Answer 2

Thank you so much for your help,it helps to clear some confusions😃😃

Answer 3

Good method of solving