Question

Consider the geometric sequence 16, 8, a, 2, b, ... (a) Write down the common
ratio. (b) Write down the value of a and b (c) Write down the nth term of the
geometric sequence. (d) Find the 8th term. *

Answer 1

Find the common ratio by dividing.

16 / 8 = 2

8 / a = 2

2 / b = 2

The common ratio is 2.

Since we need to find the values of a and b, use the common ratio to solve for them.

8 / 2 = 4 (a)

2 / 2 = 1 (b)

Now, we know that first 5 terms.

We can solve for the 8th term using the previous terms and the common ratio.

6th term: 1 / 2 = 0.5

7th term: 0.5 / 2 = 0.25

8th term: 0.25 / 2 = 0.125

Part A: 2

Part B: a = 4, b = 1

Part C: 0.125

Best of Luck!

Answer 2

The common ratio of the geometric progression is 0.5, the value of 'a' is 4, and the value of 'b' is 2 and this can be determined by using the concept of the geometric progression.

Given :

Sequence  --  16, 8, a, 2, b, ...

a) The common ratio of the geometric progression is calculated as:

$r = \dfrac{8}{16}$

$r = 0.5$

b) The value of 'a' can be calculated as:

$\begin{aligned}\\0.5 &=\dfrac{a}{8}\\a &= 4\\\end{aligned}$

The value of 'b' can be calculated as:

$\begin{aligned}\\0.5 &=\dfrac{b}{4}\\b &= 2\\\end{aligned}$

c) The nth term of the geometric progression can be calculated as:

$a_n = (0.5)^{n-1}$

d) The 8th term of the given geometric progression is:

$a_8 = (0.5)^{8-1}\\a_8 = \left(\dfrac{1}{2} \right )^7$

For more information, refer to the link given below:

https://brainly.com/question/14320920