Question

Which sequence is geometric and has 1/4 as it’s fifth term and 1/2 as common ratio is it A)...,1,1/2,1/4,1/8,...

Answer 1

A) ...,1,1/2,1/4,1/8,...

Answer 2

Answer:

Option A - $......,1,\frac{1}{2},\frac{1}{4},\frac{1}{8}...$                

Step-by-step explanation:

Given : A geometric has $\frac{1}{4}$ as its's fifth term and $\frac{1}{2}$ as common ratio.

To find : Which sequence is geometric ?

Solution :

The geometric sequence is defined as $a,ar,ar^2,ar^3...$

where, a is the first term and r is the common ratio.

The nth term of the sequence is $a_n=ar^{n-1}$

We have given, $r=\frac{1}{2}$ and  $a_5=\frac{1}{4}$

The 5'th term is

$a_5=ar^{5-1}$

$\frac{1}{4}=a(\frac{1}{2})^{4}$

$\frac{1}{4}=a(\frac{1}{16})$

$\frac{16}{4}=a$

$a=4$

The sequence form is $4,4(\frac{1}{2}),4(\frac{1}{2})^2,4(\frac{1}{2})^3,4(\frac{1}{2})^4,4(\frac{1}{2})^5...$

$4,2,1,\frac{1}{2},\frac{1}{4},\frac{1}{8}...$

From the given sequence Option A matched with result.

Therefore, Option A is correct.