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.
