Question

If x - 1, 2x + 2, and 4x + 16 are the first three terms of a geometric sequence, what is the value of x?

Answer 1

When you have a geometric sequence, you can divide any two consecutive terms and get the same number, which is called the common ratio. For you problem, this means if you divide the second term by the first, and the third by the second, you should get the same number. In other words:\[\frac{2x+2}{x-1}=\frac{4x+16}{2x+2}\]If you solve this equation, you should end up with the values of x that make that sequence geometric.

Answer 2

so its going to be 2x-2=2x+8

Answer 3

hmm...you would need to cross-multiply to solve this one I believe. You should end up with the equation:\[(2x+2)^2=(4x+16)(x-1)\]Multiply everything out, move everything to one side, then solve like a quadratic

Answer 4

so x = 2.5 or 5/2