Question

Which function below represents the arithmetic sequence 3, 7, 11, 15...?

(1 point)
• f(n) = 4 + 3(n - 1)
• f(n) = 4 + 3n
• f(n) = 3 + 4n
• f(n) = 3 + 4(n - 1)

Answer 1

[AI-generated answer — Bot GPT 3.5]

f(n) = 3 + 4(n - 1) represents the arithmetic sequence 3, 7, 11, 15...

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine the function representing the arithmetic sequence 3, 7, 11, 15..., we need to find the common difference between consecutive terms.

The common difference is calculated by subtracting the previous term from the current term. Let's evaluate the differences for the given sequence:

7 - 3 = 4
11 - 7 = 4
15 - 11 = 4

Since the differences are all equal to 4, the common difference is 4.

Now, we need to find the correct function. In an arithmetic sequence, the general formula is:

f(n) = a + (n - 1)d

Where a is the initial term and d is the common difference.

In our case, the initial term is 3, and the common difference is 4. So, the correct function that represents the arithmetic sequence 3, 7, 11, 15... is:

f(n) = 3 + 4(n - 1)

Therefore, the correct choice is:
• f(n) = 3 + 4(n - 1)

Answer 3

[AI-generated answer — Explain Bot]

To determine the function that represents the arithmetic sequence 3, 7, 11, 15..., we can observe the pattern in the sequence. In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term.

In this sequence, you can see that the difference between each term is 4. Starting with 3, if we add 4 repeatedly, we get the subsequent terms: 3 + 4 = 7, 7 + 4 = 11, 11 + 4 = 15, and so on.

To find the function that represents this arithmetic sequence, we need to find an expression that relates the term number (n) to the values in the sequence.

Let's go through the options provided:

a) f(n) = 4 + 3(n - 1)
In this function, we have 4 as a constant value added to another term. It does not match the pattern observed in the given sequence.

b) f(n) = 4 + 3n
This function includes a constant value of 4 and multiplies the term number n by 3. It does not match the pattern observed in the given sequence.

c) f(n) = 3 + 4n
This function starts with a constant value of 3 and multiplies the term number n by 4. It matches the pattern observed in the given sequence.

d) f(n) = 3 + 4(n - 1)
This function starts with a constant value of 3 and multiplies the term number (n - 1) by 4. It does not match the pattern observed in the given sequence.

Therefore, the correct function that represents the arithmetic sequence 3, 7, 11, 15... is f(n) = 3 + 4n.