Question

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

Answer 1

Any geometric sequence can be expressed as:

a(n)=ar^(n-1)  we are told that the fifth term is 1/4 and the common ratio is 1/2 so:

1/4=a(1/2)^(5-1)

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

1/4=a/16  multiply both sides by 16

16/4=a

4=a, so this sequence is:

a(n)=4(1/2)^(n-1)