SOLUTION: The question is: Three consecutive terms of a geometric sequence have a sum of 28 and a product of 512. Find these numbers. (Hint: let these numbers be a/r, a and ar ) I really

Question 212918: The question is: Three consecutive terms of a geometric sequence have a sum of 28 and a product of 512. Find these numbers.
(Hint: let these numbers be a/r, a and ar )
I really don't understand the question, anyone kindly help me??
Thanks
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
A geometric sequence looks like:
7
7*3 = 21
21*3 = 63
63*3 = 189
108*3 = 567
The sequence is:
7,21,63,189,567
In the general formula, I call the nth term
so,

etc.
The multiplier for each term, in this case, ,
is called , and
All this is saying is:

Another general formula is:

Testing the formula:

If I plug in , then I get
7,21,63,189,567
Now, refering back to your problem, they are just saying

Then, using my formula again

The sequence is:
a, ar, ar^2, ar^3, ar^4
By suggesting that you use a/r, a, and ar, what
they are doing is starting the sequence with
instead of , which still gives you a valid sequence

The sequence is
a/r, a, ar, ar^2
Using my example with ,
the terms would be:
7/3, 7, 21, 63, etc, which is still valid
Three consecutive terms of a geometric sequence have a sum of 28 and a product of 512, so
(1)
(2)

Plugging this into the 1st equation,
(1)
Multiply both sides by

Use the quadratic formua:

RELATED QUESTIONS
First question: A geometric sequence consisting of four terms in which ratio is... (answered by robertb)

Pls Help me with this question urgently,thanks. Find the three numbers in a... (answered by Edwin McCravy)

the sum and product of the three numbers in a Geometric progression are 28 and 512... (answered by stanbon)

find the first 3 terms of a geometric progression whose sum is 42 and whose product is... (answered by htmentor)

The product of three consecutive terms in a geometric sequence is -1000, and their sum is (answered by robertb)

the sum three consecutive terms of geometric progression is 26 and the product of them is (answered by stanbon)

The product of the first three terms of a geometric sequence is 3375 and there sum is 65. (answered by Mini-)

The product and sum of three consecutive terms in a Geometric Progression are 3375 and 65 (answered by stanbon)

if the product of the first three terms of a geometric is -8 and the sum is 14/3, what is (answered by sravanik2005)