Finding the Ratio

If you know two neighbouring terms, you know the ratio: divide the later one by the earlier one. In 7, 28, 112, ..., the ratio is $\frac{28}{7}$, which is 4. Check it on the next pair: $\frac{112}{28}$ is 4 as well.

The order matters. Dividing the earlier term by the later one gives 1/4, the ratio for walking backwards. The ratio can also be a fraction or negative: in 48, 12, ..., it is $\frac{12}{48} = \frac{1}{4}$, and in 2, -6, 18, ..., it is $\frac{-6}{2} = -3$, so the signs take turns.

This is also how you tell the two kinds of sequence apart. Subtract neighbours: the same answer each time means arithmetic. Divide neighbours: the same answer each time means geometric.