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
[tex]0.7 \times 2 = 1.4\\\\1.4 \times 2 = 2.8\\\\2.8 \times 2 = 5.6[/tex]
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 [tex]a_1 = 0.7[/tex] and [tex]a_2 = 1.4[/tex]
[tex]a_3 = 2.8[/tex] and [tex]a_4 = 5.6[/tex]
Common ratio can be found by:
[tex]\text {Common ratio }=\mathrm{r}=\frac{a_{2}}{a_{1}}=\frac{1.4}{0.7}=2[/tex]
[tex]\begin{array}{l}{\text { common ratio }=\mathrm{r}=\frac{a_{3}}{a_{2}}=\frac{2.8}{1.4}=2} \\\\ {\text { common ratio }=r=\frac{a_{4}}{a_{3}}=\frac{5.6}{2.8}=2}\end{array}[/tex]
Thus the common ratio is 2
