Question

(b)
Part C
For the sequence listed above, what is the arithmetic equation?

A
an=7+5(n−1)a_n=7+5\left(n-1\right)a
n
​
=7+5(n−1)



Part D
Rewrite the arithmetic sequence formula to slope-intercept form:


Make sure that you use the proper variables for slope-intercept form.

Answer 1

To rewrite the arithmetic sequence formula \( a_n = 7 + 5(n - 1) \) in slope-intercept form (which is typically \( y = mx + b \)), we start by simplifying the expression.

1. **Expand the formula**:
\[
a_n = 7 + 5(n - 1) = 7 + 5n - 5 = 5n + 2
\]

2. **Identify variables**:
- Let \( y = a_n \) (the terms of the sequence)
- Let \( x = n \) (the position in the sequence)

3. **Express it as \( y = mx + b \)**:
\[
y = 5x + 2
\]

Here, \( m = 5 \) (the slope) and \( b = 2 \) (the y-intercept).

So, the final slope-intercept form of the arithmetic sequence is:
\[
y = 5x + 2
\]