Question

What’s the explicit formula for the sequence 27, 18, 12, 8

Answer 1

The sequence is A(n) = 27*(1.5)^(n-1)

Explanation:

First, we need to see which type of sequence we have:

Differences:

27 - 18 = 9

18 - 12 = 6

the differences are different, let's try with the ratios.

27/18 = 1.5

18/12 = 1.5

12/8 = 1.5

So we have that this ratio is constant, then the sequence can be:

A(n) = 27*(1.5)^(n-1)

For n an integger number

where:

A(0) = 27*1.5^0 = 27

A(1) = 27*1.5^1 = 18

A(2) = 27*1.5^2 = 12

A(3) = 27*1.5^3 = 8

Answer 2

a(n) = 27*(2/3)^(n - 1)

Explanation:

The first four terms are 27, 18, 12, 8.

Find the common ratio:

To do this, let that ratio = r, and write and solve 27r = 18. Thus, r = 2/3.

The general explicit formula for this sequence is

a(n) = a(1)*(2/3)^(n - 1), or, since a(1) = 27, a(n) = 27*(2/3)^(n - 1)