Tell whether the sequence is arithmetic. If the sequence is arithmetic, write a function rule to represent it.
–3, –1, 1, 3,...
2,-4,6,-8,10
To determine whether a sequence is arithmetic, we need to check if there is a common difference between consecutive terms. In this case, let's calculate the differences between the terms:
(-1) - (-3) = 2
1 - (-1) = 2
3 - 1 = 2
Since the differences are all equal to 2, we can conclude that the sequence is arithmetic.
To find the function rule of an arithmetic sequence, we need to determine the pattern that relates the position of a term to its value.
Let's analyze the terms in the sequence: -3, -1, 1, 3, ...
Observing the pattern, we can see that each term is obtained by adding 2 to the previous term. So the function rule representing this arithmetic sequence is:
f(n) = -3 + (n-1) * 2
In this formula, n represents the position of the term in the sequence. For example, f(1) will give us the first term (-3), f(2) will give us the second term (-1), and so on.
looks like you are adding 2 each time, so yes, it is arithmetic
term(n) = 2n - 5