# How do you use the geometric sequence of numbers 1, 2, 4, 8,…to find r, the ratio between 2 consecutive terms?

Nov 5, 2015

$r = 2$
See explanation.

#### Explanation:

Let any term in a geometric sequence be $a$

Let the i'th term be ${a}_{i}$

Let a constant be k

Let the geometric ratio be r

The ${a}_{i} = k {r}^{i}$

${a}_{1} = k r = 1$
${a}_{2} = k {r}^{2} = 2$
${a}_{3} = k {r}^{3} = 4$

So ${a}_{i + 1} / {a}_{i} = \frac{k {r}^{i + 1}}{k {r}^{i}} = r$

So ${a}_{2} / {a}_{1} = \frac{2}{1} = r = 2$