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,...

B)...,1/4,1/2,1,2,...
C)...,1/72,1/36,1/18,1,9,
D)...,8,4,2,1,...

Answer 1

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

Answer 2

Option A -
`......,1,(1)/(2),(1)/(4),(1)/(8)...`

Explanation:

Given : A geometric has
`(1)/(4)` as its's fifth term and
`(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=(1)/(2)` and
`a_5=(1)/(4)`

The 5'th term is

`a_5=ar^(5-1)`

`(1)/(4)=a((1)/(2))^(4)`

`(1)/(4)=a((1)/(16))`

`(16)/(4)=a`

`a=4`

The sequence form is
`4,4((1)/(2)),4((1)/(2))^2,4((1)/(2))^3,4((1)/(2))^4,4((1)/(2))^5...`

`4,2,1,(1)/(2),(1)/(4),(1)/(8)...`

From the given sequence Option A matched with result.

Therefore, Option A is correct.