Question

Find the common ratio for the following numbers, then use the ratio to find the next three terms.

1) 1, -4, 16, -64

2) 9, 3, 1, 1/3

3) -3, 15, -75, 375

4) 24, 36, 54, 81

Answer 1

in a geometric sequence, the common ratio or common multiplier, is just a factor, thus to find it you could always just divide the next term by the previous term, that is

\(\bf 1st,\quad 2nd, \quad 3rd, \quad 4th\qquad \textit{common ratio}\implies \cfrac{2nd}{1st}\ or\ \cfrac{3rd}{2nd}\ or \cfrac{4th}{3rd}\)

Answer 2

I will do the first one and you can use the same procedure to answer the rest.

1) 1, -4, 16, -64

Common ratio = any term / previous term
common ratio r = -4/1 = -4
or 16/-4 = -4
or -64/16 = -4
The next three terms are:
-64 * -4 = 256;
256 * -4 = -1024;
-1024 * -4 = 4096

Answer 3

Thank you ranga that helps me a lot I really appreciate the help