Question

Which of the following functions generates the sequence 0, 2, 4, 6, ...?

Answer 1

Answer:

F(n) = 2n – 2

Step-by-step explanation:

The sequence 0, 2, 4, 6

First, let us determine if the sequence is arithmetic progression (A.P) or geometric progression (G.P)

This is illustrated:

Let us calculate the common difference (d)

Common difference (d) = 2nd term – first term

Common difference (d) = 3rd term – 2nd term

=> 2 – 0 = 2

=> 4 – 2 = 2

The common difference (d) = 2.

Common ratio (r) = 2nd term /1st term

Common ratio (r) = 3rd term /2nd term

=> 2/0 = undefined

=> 4/2 = 2

There is no common ratio.

Since we have a common difference, therefore the sequence is arithmetic progression.

Now, let us obtain an expression for the sequence.

This can be obtained by using the arithmetic progression formula as shown below:

F(n) = a + (n – 1)d

a is the first term

n is the number of term

d is the common difference.

The sequence 0, 2, 4, 6

The first term (a) = 0

Common difference (d) = 2

F(n) = a + (n – 1)d

F(n) = 0 + (n – 1)2

F(n) = 2n – 2