Question

Enter the explicit rule for the geometric sequence.



1/4, 1/2, 1, 2, 4, …

Answer 1

`a_n = ((1)/(4))2^(n-1)`

Explanation:

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is the same, and this quotient is given by q.

The explicit rule of a geometric sequence is given by:

`a_n = a_1q^(n-1)`

In which
`a_1` is the first term.

1/4, 1/2, 1, 2, 4

This means that
`a_1 = (1)/(4)`, and:

`q = (4)/(2) = (2)/(1) = (1)/((1)/(2)) = ((1)/(2))/((1)/(4)) = 2`

So the explicit rule is:

`a_n = ((1)/(4))2^(n-1)`