Answer:
d. 0.2; 0.08, 0.016, 0.0032
Step-by-step explanation:
The common ratio is the ratio of adjacent terms:
r = 2/10 = 0.4/2 = 0.2
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Multiplying the last term by this ratio gives the next term:
0.4×0.2 = 0.08
0.08×0.2 = 0.016
0.016×0.2 = 0.0032
The next 3 terms are 0.08, 0.016, 0.0032.
Answer:
Option D)
Common ration = [tex] \frac{1}{5}[/tex] = 0.2
The next three terms of the given series are: 0.08, 0.016, 0.0032
Step-by-step explanation:
We are given the following information in the question:
We are given a geometric sequence:
[tex]10, 2, 0.4, ...[/tex]
Geometric Series
We have to find the common ration of the given geometric series:
[tex]\text{Common ration} = \displaystyle\frac{\text{Second term}}{\text{First term} }=\frac{2}{10} = \frac{1}{5}[/tex]
The [tex]n^{th}[/tex] term of a geometric sequence is given by:
Formula:
[tex]a_n = a_1\timesr^{n-1},\\\text{where }a_1 \text{ is the first term of the geometric series and r is the common ratio}[/tex]
[tex]a_4 = a_1\times r^{4-1} = 10\times \bigg(\displaystyle\frac{1}{5}\bigg)^3 = 0.08\\\\a_5 = a_1\times r^{5-1} = 10\times \bigg(\displaystyle\frac{1}{5}\bigg)^4 = 0.016\\\\a_6 = a_1\times r^{6-1} = 10\times \bigg(\displaystyle\frac{1}{5}\bigg)^5 = 0.0032[/tex]
