which function describes the arithmetic sequence shown?
3,7,11,15,19,23,...
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The common difference between consecutive terms is 4, as each term is obtained by adding 4 to the previous term. Therefore, the arithmetic sequence can be described using the formula:
An = a1 + (n - 1) * d
where An is the nth term, a1 is the first term, n is the position of the term in the sequence, and d is the common difference.
In this case, the first term (a1) is 3, and the common difference (d) is 4. So the function that describes the arithmetic sequence is:
An = 3 + (n - 1) * 4
You can substitute any value for n to find the corresponding term in the sequence.
To determine the function that describes the given arithmetic sequence, we need to identify the common difference between each term.
In this sequence, each term increases by 4.
So, the common difference is 4.
Let's assume the first term is represented by 'a' and the common difference is represented by 'd'.
For the sequence 3, 7, 11, 15, 19, 23, ...
The first term (a) is 3, and the common difference (d) is 4.
Now, we can write the formula for the general term (nth term) of an arithmetic sequence:
nth term = a + (n - 1) * d
Plugging in the values:
nth term = 3 + (n - 1) * 4
Simplifying further:
nth term = 3 + 4n - 4
nth term = 4n - 1
Therefore, the function that describes the given arithmetic sequence is f(n) = 4n - 1.