Patterns and rules unit test part 1
Write a rule for the sequence
5,-4,-13,-22,...
Each term in the sequence is obtained by subtracting 9 from the previous term. Therefore, the rule for the sequence is:
nth term = nth-1 term - 9
where n is the position of the term in the sequence.
To find the rule for the given sequence 5, -4, -13, -22, ..., we need to identify the pattern.
Observing the differences between consecutive terms, we can see that the first term decreases by 9, the second term decreases by 9, and the third term decreases by 9. Thus, the pattern is that each term decreases by 9.
So, to write the rule for the sequence, we can start with the first term and subtract 9 for each subsequent term.
The rule for the sequence would be:
n-th term = 5 - 9n
In this formula, "n" represents the position of the term in the sequence, beginning with the first term as n = 1.
To find a rule for the given sequence, let's observe the differences between consecutive terms:
5, -4, -13, -22, ...
-4 - 5 = -9
-13 - (-4) = -9
-22 - (-13) = -9
...
We can observe that the common difference between consecutive terms is -9. Therefore, the rule for the given sequence is:
nth term = 5 + (-9) * (n - 1)
Where "n" represents the position of the term in the sequence.