Question

Write the recursive rule for the sequence: 21, -9, -39, -69, …

a) a1 = -1, an = an-1
b) a1 = 1, an = an-1
c) a1 = 21, an = an-1
d) a1 = -21, an = an-1

Answer 1

The correct recursive rule for the sequence 21, -9, -39, -69, … is not listed in the given options. It should be a1 = 21, an = an-1 - 30, because each term decreases by 30 from the previous one.

Step-by-step explanation:

The given sequence is 21, -9, -39, -69, … To find the recursive rule, we need to determine how to get from one term to the next. Looking at the sequence, we see that each term decreases by 30 from the previous term. Starting with the first term, a1 = 21, the following term can be found by subtracting 30, which means the nth term is an = an-1 - 30.

Therefore, the correct recursive rule for the sequence is:
a1 = 21, an = an-1 - 30.

The option that matches this rule is not listed in the provided choices, indicating a potential error. From the given choices, none match the correct rule. The correct recursive rule is essential for progressing through the sequence appropriately.