Question

Write the explicit formula for the arithmetic sequence.

3, -3, -9, -15, -21,

Answer 1

Explanation:

So explicit formula essentially is general term formula. Or a formula that when you put in a value for n, you can get that number term in the arithmetic sequence. The way this formula is written is:

`u_(n) = u_(1) + (n-1)d`

Where
`u_(n)` is the term (result of this formula) that is based on whatever value you put in for n

`u_(1)` is the first term of the sequence

n is the term number that you want

and d is the common difference

So to fill in a general formula or explicit formula all we need is
`u_(1)` and d, because this gives us a general expression for any term we choose, or for any value of n

So to find d, all we have to do is take the difference between a term in front and a term behind that term. Ill show you what I mean:

So if we consider the sequence above we can do

-3 - 3 or -9 - (-3) or 15 - (-9) or -21 -(-15) all of these will give us the value for d (we just take a term before and subtract it by the term after)

So all of these come out to a value of -6

So d = -6

`u_(1)` is just our first term so:
`u_(1)` = 3

Therefore, our explicit formula is

`u_(n) = 3 + (n-1)(-6)`