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

4, 2, 1, , , .....

Step-by-step explanation:

Fifth term (a₅) =  

Common ratio (r) =

n = 5

The formula to find the term of a geometric sequence is

a₅ = a₁r⁽ⁿ⁻¹⁾

=> = a₁*

=> = a₁*

=> = a₁*

=> = a₁*

=> = a₁*

Flip the sides of the equation

a₁* =

Multiply both sides by 16

a₁**16 = *16

Cancelling out the 16's from the top and bottom of the left side

a₁ =

=> a₁ = 4

So, first term of the geometric sequence is 4.

Common ratio =

Second term = First term * Common ratio

                      = 4*

                      =

                      = 2

Third term = Second Term * Common ratio

                  = 2 *

                  =

                  = 1

Fourth term = Third Term * Common ratio

                    = 1 *

                    =

Fifth term (given) =

So, the geometric sequence would be

4, 2, 1, , , .....