write a rule for the sequence 5, -4 ,-13,-22
To find a rule for the given sequence 5, -4, -13, -22, we can observe the pattern between consecutive terms.
We notice that each term decreases by 9 compared to the previous term.
Now, to express this pattern as a rule, we can use the concept of a linear equation. Let's assign the term numbers to the sequence, with n representing the position of the term. So, for n = 1, the first term is 5, for n = 2, the second term is -4, and so on.
Since each term decreases by 9 compared to the previous term, we can use the following formula:
Term(n) = 5 - (n-1) * 9
where n represents the position of the term in the sequence.
Therefore, the rule for the sequence 5, -4, -13, -22 is Term(n) = 5 - (n-1) * 9.
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This is an arithmetic progression with a common difference of -9
=5+(n-1)-9
=5-9n+9
=14-9n