Question

What is the recursive rule for the following sequence? -3, 6, 15, 24,......

a) an =an−1 +9
b) an =an−1 ×3
c) an =an−1 +6
d) an = an−1 ÷2

Answer 1

The recursive rule for the sequence -3, 6, 15, 24, ... is an = an-1 + 9.

Step-by-step explanation:

The recursive rule for the sequence -3, 6, 15, 24, ... is an = an-1 + 9 (option a).

This means that each term in the sequence is obtained by adding 9 to the previous term.

For example, starting with the first term -3, we can apply the recursive rule to find the second term: -3 + 9 = 6. Continuing this pattern, we can find the rest of the terms in the sequence.

Answer 2

The recursive rule for the sequence -3, 6, 15, 24, ... is an = an-1 + 9, which is a consistent increase of 9 between successive terms.

Step-by-step explanation:

The sequence provided is -3, 6, 15, 24, .... To find the recursive rule, look at the difference between successive terms:

• 6 - (-3) = 9
• 15 - 6 = 9
• 24 - 15 = 9

This shows that each term is 9 more than the previous term. Therefore, the recursive rule for the sequence is an = an-1 + 9, which corresponds to option a).