Tell whether the sequence is arithmetic. If the sequence is arithmetic, write a function rule to represent it.
−3, −1, 1, 3,...
clearly, a = -3
and d = 2
as always, a_n = a + (n-1)d
Yes, the given sequence is arithmetic.
To determine the function rule, we can notice that each term is obtained by adding 2 to the previous term.
So, the function rule to represent the arithmetic sequence is:
nth term = -3 + (n - 1) * 2
where n represents the position of the term in the sequence.
To determine whether a sequence is arithmetic, we need to check if the difference between consecutive terms is constant.
In this sequence, the difference between consecutive terms is always 2. Therefore, the sequence is arithmetic.
To write a function rule to represent the arithmetic sequence, we can use the general formula for arithmetic sequences, which is:
an = a1 + (n - 1) * d
where:
- an represents the n-th term of the sequence
- a1 represents the first term of the sequence
- n represents the position of the term in the sequence
- d represents the common difference between consecutive terms
In this case, we can plug in the given values into the formula:
a1 = -3 (first term)
d = 2 (common difference)
The function rule to represent the given arithmetic sequence is:
an = -3 + (n - 1) * 2
Are the numbers going up or going down?
How much is it going up by or how much is it going down by?