The sequence shown below is defined using a recursion formula. Write the first four terms of the sequence.
a Subscript 1equals2 and a Subscript nequalsa Subscript n minus 1plus4 for ngreater than or equals2


To find the first four terms of the sequence defined by the given recursive formula:

\[
a_1 = 2 \quad \text{and} \quad a_n = a_{n-1} + 4 \quad \text{for } n \geq 2,
\]

we proceed as follows:

### Step-by-step solution:

1. **First term:** 
   \[
   a_1 = 2
   \]

2. **Second term:** 
   \[
   a_2 = a_1 + 4 = 2 + 4 = 6
   \]

3. **Third term:** 
   \[
   a_3 = a_2 + 4 = 6 + 4 = 10
   \]

4. **Fourth term:** 
   \[
   a_4 = a_3 + 4 = 10 + 4 = 14
   \]

### Final Answer:
The first four terms of the sequence are:
\[
2, 6, 10, 14
\]

Would you like to see a graph of the sequence or details about the recursive growth? Here are five related questions to expand this concept:

1. How would you generalize this sequence to find any term \( a_n \) without recursion?
2. What type of sequence is this, and how can you prove it?
3. Can you calculate the sum of the first \( n \) terms of this sequence?
4. How does the sequence change if the increment is modified (e.g., to \( +3 \) instead of \( +4 \))?
5. How does this sequence relate to an arithmetic progression in general?

**Tip:** Always verify recursion formulas by calculating multiple terms to ensure consistency.

The sequence shown below is defined using a recursion formula. Write the first four terms of the sequence. a₁ = 2 and aₙ = aₙ₋₁ + 4 for n ≥ 2.

Discover how to find the first four terms of the sequence defined by a₁ = 2 and aₙ = aₙ₋₁ + 4 for n ≥ 2. Learn the step-by-step process and key concepts behind recursive and arithmetic sequences. Suitable for Grades 6-8 students.

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