Which of the following equations defines the nth term of f?  A. �(�) = 7 − 5(� − 1) for � ≥ 1
B. �(�) = 7 − 5� for � ≥ 1
C. �(�) = 7 ∙ 5(789) for � ≥ 1
D. �(�) = 7 ∙ 57 for � ≥ 1

Let's analyze each equation to see which one defines the nth term of the function \( f(n) \).

### Option A: \( f(n) = 7 - 5(n - 1) \) for \( n \geq 1 \)
This equation defines the nth term as:
\[
f(n) = 7 - 5(n - 1) = 7 - 5n + 5 = 12 - 5n
\]
So, the function for this option is \( f(n) = 12 - 5n \).

### Option B: \( f(n) = 7 - 5n \) for \( n \geq 1 \)
This equation is already simplified. It defines the nth term as \( f(n) = 7 - 5n \).

### Option C: \( f(n) = 7 \cdot 5(789) \) for \( n \geq 1 \)
This option seems unclear or possibly incomplete. The term \( 5(789) \) appears to be a constant multiplication, making the equation \( f(n) = 7 \cdot 5(789) \), which would result in a constant value for all \( n \).

### Option D: \( f(n) = 7 \cdot 57 \) for \( n \geq 1 \)
This equation is a constant function, with the nth term always equal to \( 7 \times 57 = 399 \), regardless of \( n \).

### Conclusion:
The correct answer is **Option B**: \( f(n) = 7 - 5n \) for \( n \geq 1 \), as it presents a linear relationship for the nth term.

Would you like more details on why Option B is correct or have any further questions?

Here are 5 related questions to deepen your understanding:
1. How do you derive the nth term of an arithmetic sequence?
2. What is the significance of \( n \geq 1 \) in defining a sequence?
3. Can a sequence be constant, and how do you identify such a sequence?
4. How do different forms of linear equations relate to sequences?
5. What are the differences between recursive and explicit formulas for sequences?

**Tip**: Always check if an equation simplifies into a recognizable pattern, such as arithmetic or geometric sequences, to understand the behavior of the nth term.

Which of the following equations defines the nth term of f? A. f(n) = 7 − 5(n − 1) for n ≥ 1 B. f(n) = 7 − 5n for n ≥ 1 C. f(n) = 7 ∙ 5(789) for n ≥ 1 D. f(n) = 7 ∙ 57 for n ≥ 1

This problem focuses on identifying the correct equation for the nth term of a sequence. Explore options like f(n) = 7 - 5n and learn how to derive a linear relationship. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation