Question

Which sequence is geometric and has 1/4 as its fifth term and 1/2 as the common ratio?

Answer 1

5th term = a1r^4 where a1 = first term and r = common ratio

so 1/4 = a1 * (1/2)^4

a1 = 1/4 / (1/2)^4 = 4

so the sequence is 4 , 4*1/2, 4*(1/2)^2...

= 4, 2, 1, 1/2, 1/4 .....

Answer 2

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

Explanation:

Since explicit formula of a geometric sequence is represented by An =
`A_(1)(r)^(n-1)`

It is given in the question that fifth term of the sequence is
`((1)/(4))` and common ratio of the sequence is
`(1)/(2)`.

Now from the explicit formula

`A_(5)=(1)/(4) =A_(1)((1)/(2))^(5-1)`

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

`A_(1) (2^(4) )/(4)`

`(16)/(4)` = 4

Therefore, sequence will be 4, 4 ×
`((1)/(2))`, 4 ×
`(1)/(2)^(2)`, 4 ×
`((1)/(2))`³.........

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