The first term of a geometric progression is 16 and the last term is 11664. If the sum of all the terms is 17488, determine the number of geometric means between 16 and 11664.

Question

anonymous · Answer

very easy
use the formula for g.p. and sum of g.p.
solve for r and then a

anonymous · Answer

How do you solve for r?

anonymous · Answer

Let a be the first number, so a=16.
The last number is
$$
16 r^k =11664 \
r^k= 729= 3^6\
$$
r=3 and k=6
So there are 7 terms
You really do not need to have the sum as given.

anonymous · Answer

$$
Sum= \frac{a \left(r^{k+1}-1\right)}{r-1}=\frac{16
   \left(3^7-1\right)}{3-1}=17488
$$
So you do not need that sum to be given to solve the problem. In fact, you can find it.

anonymous · Answer

Here are the seven terms
$$
{16, 48, 144, 432, 1296, 3888, 11664}
$$