Question

Determine the common ratio and find the next three terms of the geometric sequence.

Answer 1

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 2

Answer:

Option D)

Common ration = $\frac{1}{5}$ = 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:

$10, 2, 0.4, ...$

Geometric Series

• A geometric series is a series with a constant ratio between successive terms

We have to find the common ration of the given geometric series:

$\text{Common ration} = \displaystyle\frac{\text{Second term}}{\text{First term} }=\frac{2}{10} = \frac{1}{5}$

The $n^{th}$ term of a geometric sequence is given by:

Formula:

$a_n = a_1\timesr^{n-1},\\\text{where }a_1 \text{ is the first term of the geometric series and r is the common ratio}$

$a_4 = a_1\times r^{4-1} = 10\times \bigg(\displaystyle\frac{1}{5}\bigg)^3 = 0.08\\\\a_5 = a_1\times r^{5-1} = 10\times \bigg(\displaystyle\frac{1}{5}\bigg)^4 = 0.016\\\\a_6 = a_1\times r^{6-1} = 10\times \bigg(\displaystyle\frac{1}{5}\bigg)^5 = 0.0032$