Question

Which function describes the arithmetic sequence shown?

7, 9, 11, 13, 15, 17, ...
A) ƒ(x) = 2x − 5
B) ƒ(x) = 5x − 2
C) ƒ(x) = 2x + 5
D) ƒ(x) = 5x + 2

Answer 1

2X + 5

Explanation:

1st. 2 × 1 + 5 => 7

2nd. 2 × 2 + 5 => 7

3rd. 2 × 3 + 5 => 7

4th. 2 × 4 + 5 => 7

5th. 2 × 5 + 5 => 7

6th. 2 × 6 + 5 => 7

Xth. 2 × X + 5 => 2X + 5

Answer 2

The function that describes the arithmetic sequence is C)
`f(x) = 2x + 5`.

Explanation:

A sequence is a set of numbers that are in order.

An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.

If the first term of an arithmetic sequence is
`a_1` and the common difference is
`d`, then the x th term of the sequence is given by

`y_(x)=a_(1)+(x-1)d`

7, 9, 11, 13, 15, 17, ... is an arithmetic sequence with the common difference 2.

The values of
`a_1` and
`d` are:

`a_1=7\\\\d=2`

Using the Arithmetic Sequence formula:

`y_(x)=7+(x-1)\cdot 2\\\\y_(x)=7+\left(2x-2\right)\\\\y_(x)=2x+5`