What's the explicit rule for the sequence 9 14 19 24?

The explicit rule for the arithmetic sequence 9, 14, 19, 24 is a_n = 9 + 5(n - 1).

Understanding Arithmetic Sequences and Explicit Rules

An arithmetic sequence is a sequence where the difference between consecutive terms is constant. This constant difference is called the common difference. In the given sequence, 9, 14, 19, 24, the common difference is 5 (14 - 9 = 5, 19 - 14 = 5, and so on).

The explicit rule (or explicit formula) allows you to directly calculate any term in the sequence without needing to know the previous terms.

The General Formula

As stated in the reference, the general formula for an arithmetic sequence is:

a_n = a₁ + d(n - 1)

Where:

• a_n is the nth term of the sequence
• a₁ is the first term of the sequence
• d is the common difference
• n is the term number

Applying the Formula to the Sequence 9, 14, 19, 24

1. Identify a₁: The first term (a₁) is 9.

2. Identify d: The common difference (d) is 5.

3. Substitute into the formula:

   a_n = 9 + 5(n - 1)

Therefore, the explicit rule for the sequence 9, 14, 19, 24 is a_n = 9 + 5(n - 1).

Example Calculation

Let's find the 4th term using the explicit rule:

a₄ = 9 + 5(4 - 1)
a₄ = 9 + 5(3)
a₄ = 9 + 15
a₄ = 24

This confirms that the explicit rule correctly calculates the 4th term, which is indeed 24.