SOLUTION: the numbers a, b, c are the terms of a geometric sequence so that a+b+c=35 and abc=1000 find a, b and c

Question 3840: the numbers a, b, c are the terms of a geometric sequence so that
a+b+c=35 and abc=1000
find a, b and c
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
a nice little question :-)

Let first term = a
then second term = ar
and third term =

where r is the common ratio.

And we know that all 3 terms multiplied together = 1000. So,

--> ar = cube root of 1000
ie ar = 10.

And ar, by definition is the number b. So we have one found.

Since abc = 1000 and b=10, then ac=100. We shall use this in a moment.

Also, a+b+c=35. So now this becomes a+c=25 or a=25-c. Now sub this into the ac=100, to give (25-c)c=100.

Multiplying this out, we get a quadratic, which factorises to (c-5)(c-20)=0, so c=5 or c=20. This means that a=20 or a=5...ie the reverse solution. So,

a=5
b=10
c=20

Common ratio is 2.
and Adding them --> 35
multiplying them --> 1000.

jon

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