Question

In a geometric sequence, the_between consecutive terms is constant.

Answer 1

Answer:

In a geometric sequence, the common ratio between consecutive terms is constant.

Step-by-step explanation:

In a geometric sequence, the common ratio between consecutive terms is constant.

The n-th term of a geometric sequence with first term $a$ and common ratio $r$ is represented by the formula:

$a_{n}=a\,r^{n-1}$

For example,

$1, -3, 9, -27, 81, -243, ...$

As the common ratio 'r' between consecutive terms is constant.

• r = -3/1 = -3

• r = 9/-3 = -3

• r = -27/9 = -3

• r = 81/-27 = -3

• r = -243/81 = -3

So, the common ratio between consecutive terms is constant i.e. -3. Thus, it is a geometric sequence with a common ratio -3.