Write a rule to the sequence.
8, -1, -10, -19, …
The sequence appears to be decreasing by 9 each time. So, the rule for the sequence is to subtract 9 from the previous term to get the next term. Therefore, the rule is:
a(n) = a(n-1) - 9, where a(1) = 8.
Using this rule, the next few terms in the sequence would be:
a(5) = a(4) - 9 = -19 - 9 = -28
a(6) = a(5) - 9 = -28 - 9 = -37
To determine the rule for the given sequence, let's analyze the differences between consecutive terms:
-1 - 8 = -9
-10 - (-1) = -9
-19 - (-10) = -9
We observe that the differences between consecutive terms are always -9. Therefore, the rule for this sequence can be expressed as follows:
Start with 8 and subtract 9 from the previous term to get the next term.
So, the next term in the sequence would be:
-19 - 9 = -28