Question

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

10, 2, 0.4, ...



a.

0.2; -0.4, -2, -10

c.

0.02; 0.08, 0.016, 0.0032


b.

0.02; -0.4, -2, -10

d.

0.2; 0.08, 0.016, 0.0032

Answer 1

Option D)

Common ration =
`(1)/(5)` = 0.2

The next three terms of the given series are: 0.08, 0.016, 0.0032

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} }=(2)/(10) = (1)/(5)`

The
`n^(th)` term of a geometric sequence is given by:

Formula:

`a_n = a_1*r^(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* r^(4-1) = 10* \bigg(\displaystyle(1)/(5)\bigg)^3 = 0.08\\\\a_5 = a_1* r^(5-1) = 10* \bigg(\displaystyle(1)/(5)\bigg)^4 = 0.016\\\\a_6 = a_1* r^(6-1) = 10* \bigg(\displaystyle(1)/(5)\bigg)^5 = 0.0032`

Answer 2

d. 0.2; 0.08, 0.016, 0.0032

Explanation:

The common ratio is the ratio of adjacent terms:

r = 2/10 = 0.4/2 = 0.2

__

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.