Chapter 12, Problem 1RE

To determine

Whether the statement “In a geometric sequence, the ratio between any two consecutive terms is a constant” is true or false.

Answer to Problem 1RE

The statement “In a geometric sequence, the ratio between any two consecutive terms is a constant” is $\underset{\_}{\text{true}}$.

Explanation of Solution

The given statement is “In a geometric sequence, the ratio between any two consecutive terms is a constant”.

From definition it is clear that in a geometric sequence the first term can be found by multiplying the preceding term by the same number and the ratio of any two consecutive terms is a constant r.

It is given by $r=\frac{a_{n+1}}{a_n}\left(\because n\ge 1\right)$.

Therefore, the statement “In a geometric sequence, the ratio between any two consecutive terms is a constant” is $\underset{\_}{\text{true}}$.