What function represents the arithmetic sequence 3,7,11,15?
What do you think is the answer, Steve?
f(n) =3 +4(n-1)
I think you are correct, Steve. It looks right to me.
Thank you
You're welcome, Steve. :)
To determine the function that represents an arithmetic sequence, we need to identify the common difference between consecutive terms.
In this sequence, the common difference between each term is 4. Notice that by adding 4 to the previous term, we get the next term in the sequence.
We can use this information to determine the function. Let's denote the first term of the sequence as a and the common difference as d.
The first term, a, is 3, and the common difference, d, is 4. Therefore, the nth term of the sequence can be represented by the formula:
an = a + (n-1) * d
Plugging in the values from the sequence, we have:
an = 3 + (n-1) * 4
Simplifying further:
an = 3 + 4n - 4
an = 4n - 1
So, the function that represents the arithmetic sequence 3, 7, 11, 15 is:
an = 4n - 1.