Question

1. what is the common difference in this recursive definition?

\\(a_1 = \frac{4}{7}\\)
\\(a_n = a_{n-1} + \frac{1}{7}\\)

\\(d = a_{n-1}\\)
\\(d = \frac{1}{7}\\)
\\(d = \frac{4}{7}\\)
\\(d = -\frac{1}{7}\\)

Explanation:

⚡ Using what you learned: Arithmetic Sequences · Recursive and Explicit Formulas

Step 1: Identify the recursive formula structure

The given recursive definition is:

$$ a_1 = 4 $$

$$ a_n = a_{n-1} + \frac{2}{7} $$

The general recursive formula for an arithmetic sequence is:

$$ a_n = a_{n-1} + d $$

where \( d \) represents the common difference.

Step 2: Determine the value of \( d \)

By comparing the given formula to the general form:

$$ a_n = a_{n-1} + \frac{2}{7} $$

We find:

$$ d = \frac{2}{7} $$

Answer:

\( d = \frac{2}{7} \)