Question

Consider the arithmetic sequence 10,12,14,16 if n is an integer, which of these functions generate the sequence?

Answer 1

Given:

The arithmetic sequence is:

10, 12, 14, 16, ...

To find:

The function that generates the given sequence if n is an integer.

Solution:

We have,

10, 12, 14, 16, ...

Here, the first term is 10 and the common difference is:

`d=a_2-a_1`

`d=12-10`

`d=2`

The nth term of an arithmetic sequence is:

`a_n=a+(n-1)d`

Where, a is the first term, d is the common difference and
`n\geq 1`.

Putting
`a=10,d=2` in the above formula, we get

`a_n=10+(n-1)2`

`a_n=10+2n-2`

`a_n=8+2n`

Therefore, the function
`a_n=8+2n, n\geq 1` generates the sequence.