Question

Write an equation for the nth term of each geometric sequence. (show work)

1. 1, 4, 16, ...
2. 1, 1/2, 1/4, ...
3. 7, -14, 28, ...

Answer 1

1) 4n

The arithmetic sequence is going up in 4’s (1 x 4 = 4, 4 x 4 = 16)
Therefore the answer is just 4n

2) 0.5n (1/2n)
The arithmetic sequence is going up in 0.5’s (1 x 0.5 = 1/2, 1/2 x 0.5 = 1/4)
Therefore the answer is just 0.5n or if you need it in a fraction it is (1/2n)

3) -7n
The arithmetic sequence is going up in -7’s (7 x -7 = -14, -14 x -7 = 28)
Therefore the answer is just -7n