Question

Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 20 10. 5

Answer 1

Given:

Consider the given terms of the sequence are:

20, 10, 5, ...

To find:

The type of sequence (arithmetic or geometric) and the common difference / ratio in simplest form.

Solution:

We have,

20, 10, 5, ...

Difference between consecutive terms are:

$10-20=-10$

$5-10=-5$

Since $-10\neq -5$, therefore the given sequence has no common difference, it means the given sequence is not arithmetic.

Ratio between consecutive terms are:

$\dfrac{10}{20}=\dfrac{1}{2}$

$\dfrac{5}{10}=\dfrac{1}{2}$

The given sequence has a common ratio $\dfrac{1}{2}$, it means the given sequence is a geometric sequence.

Therefore, the given sequence is a geometric sequence with common ratio $\dfrac{1}{2}$ it is also written as 0.5.