Solution #7

Let the first term of the geometric sequence be a, and the ratio be r. Then the first five terms of the sequence are a, ar, ar², a³, and a⁴.

So we have:

ar - a = 9
ar⁴-ar³=576

From the first, we have a(r-1)=9.

Factoring the second, we have:

r³a(r-1)=576

Substitution 9 for a(r-1), we have:

r³=576
r=4

So 4a - a = 9, and a = 3.

Thus the first five members of the sequence are 3, 12, 48, 192, and 768, and their sum is 1023.