How to find numerical value (question about geometric sequence) plz help...plz?

Question

The first three terms of geometric sequence are x, x+5 and x+9. Determine the numerical value of the first three terms.

Answer 1

What an odd question.

Each successive term of a geometric sequence is the product of the previous term and a constant.  Let the constant be 'r', then

x + 5 = rx

and

x + 9 = r(x + 5) = xr^2

So, xr^2 = x + 9

xr^2 - x = 9

x(r^2 - 1) = 9

and

r(x + 5) = xr^2

xr + 5r = xr^2

xr^2 - xr = 5

x(r^2 - r) = 5

We have two unknowns - x and r.  Now we have two equations for them.  This can be solved.  I'll leave the rest of the solution to you.  I would suggest solving them both for x and substituting.