The given sequence is:

$10, 14, 18, 22, 26, \dots$

We need to find the recursive formula for this arithmetic sequence.

Step 1: Identify the first term $a_1$

The first term $a_1 = 10$.

Step 2: Find the common difference

The difference between consecutive terms is: $14 - 10 = 4$ So, the common difference $d = 4$.

Step 3: Determine the recursive formula

In an arithmetic sequence, the recursive formula is generally given by: $a_n = a_{n-1} + d$ Where $d$ is the common difference.

Since $d = 4$ and $a_1 = 10$, the recursive formula becomes: $a_n = a_{n-1} + 4$

Now, let's check the options:

• Option A: $a_1 = 30$, $a_n = a_{n-1} + 4$ → Incorrect because $a_1$ is not 30.
• Option B: $a_1 = 10$, $a_n = a_{n-1} + 4$ → Correct, matches the sequence.
• Option C: $a_1 = 4$, $a_n = a_{n-1} + 10$ → Incorrect, neither $a_1$ nor the common difference is correct.
• Option D: $a_1 = 10$, $a_n = a_{n-1} - 4$ → Incorrect, the common difference should be +4, not -4.

Final Answer:

The correct option is B.

Would you like further details or have any questions?

Here are 5 questions for further exploration:

1. How can you convert a recursive formula into an explicit formula?
2. What is the general form of a recursive formula for arithmetic sequences?
3. Can you find the 10th term of this sequence using the recursive formula?
4. What happens if the common difference is negative in an arithmetic sequence?
5. How can recursive formulas be used in solving real-life problems?

Tip: Always check both the first term and the common difference when determining recursive formulas for arithmetic sequences.