Question

To show that arithmetic sequence formulas have the same structure as linear functions, choose the linear function equation that has the same structure as the arithmetic sequence An=6+(n-1)*8

y=8x+6

y=6x+8

y=2x-8

y=8x-2

Answer 1

Let's start by analyzing the given arithmetic sequence formula:

\[ A_n = 6 + (n - 1) * 8 \]

We can simplify this expression:

1. Distributing the 8:
\[ A_n = 6 + 8n - 8 \]

2. Combine like terms:
\[ A_n = 8n - 2 \]

Now we can compare this with the standard form of a linear function, which is typically represented as:

\[ y = mx + b \]

In the simplified form, we can see:

- The slope \( m \) is 8.
- The y-intercept \( b \) is -2.

Thus, the corresponding linear function that shares the same structure as the arithmetic sequence is:

\[ y = 8x - 2 \]

So the correct answer from the choices provided is:

**y = 8x - 2**.