Question

Which explicit formula is equivalent to a1 = 1, an=

4an-1?
A. an = 1(4)^n-1
B. an = 4(4)^n-1
C. an = 4(1)^n–1
D. an = 1 + (n - 1)4

Answer 1

A. an = 1(4)^n-1

Explanation:

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is always the same, called common ratio, and the sequence is given by:

`a_n = a_1(q)^(n-1)`

In which
`a_1` is the first term and q is the common ratio.

We are given the following sequence:

`a_1 = 1`

`a_n = 4a_(n-1)`

So

`a_2 = 4a_1 = 4`

`a_3 = 4a_2 = 16`

`a_4 = 4a_3 = 64`

That is, the quotient between consecutive terms is 4, so
`q = 4`.

The first term is already given,
`a_1 = 1`. So

`a_n = a_1(q)^(n-1)`

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

And thus, the correct answer is given by option A.