Which function describes the arithmetic sequence shown?
3, 7, 11, 15, 19, 23, .....
*

f(x)= 4x - 4
f(x) = 4x - 3
f(x) = 4x - 2
f(x) = 4x -1
Manny overdrew his bank a

The given sequence is:  
3, 7, 11, 15, 19, 23, ...

To determine the function that describes the arithmetic sequence, we need to find both the common difference and the general form of an arithmetic sequence.

### Step 1: Identify the common difference.
To find the common difference, subtract any two consecutive terms in the sequence:  
\( 7 - 3 = 4 \),  
\( 11 - 7 = 4 \),  
\( 15 - 11 = 4 \),  
and so on.

Thus, the common difference \(d = 4\).

### Step 2: General form of an arithmetic sequence.
The general formula for the nth term of an arithmetic sequence is:  
\[
a_n = a_1 + (n - 1)d
\]
where:
- \(a_1\) is the first term (which is 3 in this case),
- \(d\) is the common difference (which is 4),
- \(n\) is the term number.

Using the formula:
\[
a_n = 3 + (n - 1)4
\]
Simplifying:
\[
a_n = 3 + 4n - 4
\]
\[
a_n = 4n - 1
\]

### Step 3: Match to the given functions.
The function that describes the sequence is:
\[
f(x) = 4x - 1
\]

So, the correct answer is:
\[
f(x) = 4x - 1
\]

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### Related Questions:
1. What is the general formula for an arithmetic sequence?
2. How do you determine the common difference in an arithmetic sequence?
3. What is the difference between an arithmetic sequence and a geometric sequence?
4. How do you find the sum of the first \(n\) terms of an arithmetic sequence?
5. What changes in the formula if the sequence starts from a different first term?

### Tip:
Always check the first few terms when plugging values into your function to confirm the accuracy.

Which function describes the arithmetic sequence shown? 3, 7, 11, 15, 19, 23, .....

Explore how to find the function that describes the arithmetic sequence 3, 7, 11, 15, 19, 23 using the general formula for arithmetic sequences. This problem involves identifying the common difference and deriving the linear function. Suitable for Grades 6-8.

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