Question

Which function defines the sequence 6,8,10,?

Answer 1

Answer:

$a_{n} =2n+4$

Step-by-step explanation:

In order to find the function satisfies all terms, you must first start off by finding the common difference between each of the terms you have been given.

In order to get from 6 to 8 and from 8 to 10, you add 2. So 2 is your common difference.

The easiest way to find your function is to use an explicit function.

You will start with the point-slope formula: y-y1=m(x-x1) and you can use the first number stated as a coordinate to plug in. The number given in the sequence will be your y-value, but notice how there is no x value. In problems like these, unless explicitly stated, you can always assume that the first number is the first term, which has an x value of 1. So your coordinate to plug in will be (1,6). Your common difference is going to be your m or slope value. Plug it into the point-slope formula...

y-6=2(x-1)

distribute

y-6=2x-2

add 6 to both sides

y=2x+4

Now that you have your equation, you can just replace y with $a_{n}$ (that just means "any term in the sequence") and you can replace x with n (that just means the term you want to find)

Your final function is

$a_{n} =2n+4$

This is the function you would use to find any term in that sequence