Question

Стоито

Find the common ratio for this geometric sequence.
0.7, 1.4, 2.8, 5.6, ...
ОА. 0.5
Ов. 0.75
Ос. 2
OD. -2

Answer 1

Option C

The common ratio for this geometric sequence 0.7, 1.4, 2.8, 5.6, ... is 2

Solution:

Given geometric sequence is:

0.7, 1.4, 2.8, 5.6, ...

To find: common ratio for this geometric sequence

A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, "r"

In the given sequence, the next term in squence is found out by multiplying previous term by 2

`0.7 * 2 = 1.4\\\\1.4 * 2 = 2.8\\\\2.8 * 2 = 5.6`

So the common ratio in given sequence is 2

Method 2:

Given geometric sequence is:

0.7, 1.4, 2.8, 5.6, ...

Here first term
`a_1 = 0.7` and
`a_2 = 1.4`

`a_3 = 2.8` and
`a_4 = 5.6`

Common ratio can be found by:

`\text {Common ratio }=\mathrm{r}=(a_(2))/(a_(1))=(1.4)/(0.7)=2`

`\begin{array}{l}{\text { common ratio }=\mathrm{r}=(a_(3))/(a_(2))=(2.8)/(1.4)=2} \\\\ {\text { common ratio }=r=(a_(4))/(a_(3))=(5.6)/(2.8)=2}\end{array}`

Thus the common ratio is 2