https://file.aiquickdraw.com/mathbot/file/1730237132817gciihk4m.jpg

The image shows a recursive sequence definition:

1. The initial term is given by:
   \[
   a_1 = 2
   \]

2. The recursive formula is:
   \[
   a_n = a_{n-1} + 5
   \]

This defines an arithmetic sequence where each term is obtained by adding 5 to the previous term.

To express this sequence in a general (explicit) form, we can use the formula for an arithmetic sequence:
\[
a_n = a_1 + (n - 1) \cdot d
\]
where \( a_1 = 2 \) and the common difference \( d = 5 \).

Thus, the explicit formula for \( a_n \) is:
\[
a_n = 2 + (n - 1) \cdot 5
\]
which simplifies to:
\[
a_n = 5n - 3
\]

### Would you like further details on how this formula was derived?

Here are some related questions that expand on this information:

1. What is the 10th term of this sequence?
2. How do we find the sum of the first \( n \) terms of an arithmetic sequence?
3. How does a recursive formula differ from an explicit formula?
4. How would the sequence change if the initial term were different?
5. What is the general solution for an arithmetic sequence given any starting value and common difference?

**Tip:** In arithmetic sequences, each term increases or decreases by a fixed number. Use the explicit formula to quickly find terms without calculating each one recursively.

Given the recursive sequence defined as a₁ = 2 and aₙ = aₙ₋₁ + 5, find the explicit formula for the sequence.

Learn how to find the explicit formula for a recursive sequence where a₁ = 2 and each term is generated by adding 5 to the previous term. This sequence is arithmetic, and the solution involves applying the formula for arithmetic sequences. Suitable for students in Grades 8-10.

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