Let's go through the worksheet step-by-step.

Part A: Identifying the Next Term in the Sequence

For each sequence provided, we need to find the next term using the given options:

1. Sequence: $3, 7, 11, 15, \ldots$

   • This sequence increases by 4 each time. So, the next term is $15 + 4 = 19$.

2. Sequence: $3, 6, 12, 24, \ldots$

   • This sequence doubles each time. So, the next term is $24 \times 2 = 48$.

3. Sequence: $7, 4, 1, -2, \ldots$

   • This sequence decreases by 3 each time. So, the next term is $-2 - 3 = -5$.

4. Sequence: $-1, 4, -9, 16, \ldots$

   • The sequence alternates between positive and negative perfect squares. The next term is $-25$.

Answers for Part A:

1. $19$
2. $48$
3. $-5$
4. $-25$

Part B: Completing the Equations/Formulas

1. Sequence: $3, 5, 7, \ldots$

   • The formula given is $a_n = 2n + 1$.

2. Sequence: $5, 10, 15, 20, \ldots$

   • The formula is $a_n = 5n$.

3. Sequence: $2, 7, 12, \ldots$

   • The formula follows $a_n = 5n - 3$.

4. Sequence: $5, 8, 13, 20, \ldots$

   • The formula is $a_n = n^2 + 4$.

Would you like more details or have any specific questions about these sequences?

Related Questions

1. What is the general formula for an arithmetic sequence?
2. How do you determine if a sequence is arithmetic or geometric?
3. How can you derive a formula for a quadratic sequence?
4. What is the formula for the $n$-th term of a geometric sequence?
5. How do you identify alternating sequences?

Tip

When finding the next term in a sequence, observe if the sequence is arithmetic, geometric, or follows a specific pattern like alternating signs or powers.