Asked by adaleta



Use the explicit formula to identify:

What type of sequence is it? Arithmetic or Geometric?

Answered by adaleta
very short
Answered by adaleta
short

The cheerleaders at a football game launch T-shirts into the crowd from the back of a golf cart that is 2 feet off the ground. The T-shirts have an upward velocity of 30 feet per second. Using the function , identify the y-intercept and explain its meaning.
Answered by adaleta
What is the common difference or common ratio?The cheerleaders at a football game launch T-shirts into the crowd from the back of a golf cart that is 2 feet off the ground. The T-shirts have an upward velocity of 30 feet per second. Using the function , identify the y-intercept and explain its meaning.

Answered by adaleta
very short
Answered by adaleta


Use the explicit formula to identify:

What type of sequence is it? Arithmetic or Geometric?
Answered by GPT-4o mini
To identify whether a sequence is arithmetic or geometric, we need to look at the explicit formula provided for the sequence. However, since you haven't provided a specific formula, I can explain the characteristics of each type:

1. **Arithmetic Sequence**:
- An arithmetic sequence has a constant difference between consecutive terms. The explicit formula for an arithmetic sequence can be written as:
\[
a_n = a_1 + (n-1)d
\]
where \( a_n \) is the \(n\)-th term, \( a_1 \) is the first term, \( d \) is the common difference, and \( n \) is the term number.

2. **Geometric Sequence**:
- A geometric sequence has a constant ratio between consecutive terms. The explicit formula for a geometric sequence can be written as:
\[
a_n = a_1 \cdot r^{(n-1)}
\]
where \( a_n \) is the \(n\)-th term, \( a_1 \) is the first term, \( r \) is the common ratio, and \( n \) is the term number.

To determine the type of sequence based on a specific explicit formula, you would need to identify if the formula follows the format of an arithmetic sequence or a geometric sequence.

If you have a specific explicit formula for the sequence, please provide it, and I can help you determine whether it is arithmetic or geometric.
Answered by GPT-4o mini
To identify the type of sequence from an explicit formula:

- **Arithmetic Sequence**: If the formula is of the form \( a_n = a_1 + (n-1)d \) (constant difference).

- **Geometric Sequence**: If the formula is of the form \( a_n = a_1 \cdot r^{(n-1)} \) (constant ratio).

Please provide the explicit formula for a specific determination.
Answered by GPT-4o mini
To identify the y-intercept of the function describing the T-shirt's motion, we typically assume a quadratic function of the form:

\[
h(t) = -16t^2 + v_0t + h_0
\]

where:
- \( h(t) \) is the height at time \( t \),
- \( v_0 \) is the initial velocity (30 ft/s),
- \( h_0 \) is the initial height (2 ft off the ground).

So, the equation is:

\[
h(t) = -16t^2 + 30t + 2
\]

### Y-Intercept:
The y-intercept occurs when \( t = 0 \):

\[
h(0) = -16(0)^2 + 30(0) + 2 = 2
\]

### Meaning:
The y-intercept (\(2\) feet) represents the initial height of the T-shirts when launched from the golf cart.
Answered by GPT-4o mini
In the context of the problem you provided, we are examining the motion of T-shirts launched into the air. This scenario does not directly involve sequences with a common difference or common ratio since these terms apply to arithmetic and geometric sequences, respectively.

### Understanding the Motion:

In the situation you described, we can model the height of the T-shirts as a function of time using a quadratic equation:

\[
h(t) = -16t^2 + 30t + 2
\]

### Key Characteristics:

1. **Y-Intercept**:
- The y-intercept occurs when \( t = 0 \):
\[
h(0) = -16(0)^2 + 30(0) + 2 = 2
\]
- **Meaning**: The y-intercept of \(2\) feet signifies the initial height of the T-shirts when they are launched, indicating that the T-shirts start at a height of \(2\) feet from the ground.

2. **Common Difference/Ratio**:
- In this scenario, we do not have a common difference (as in an arithmetic sequence) or a common ratio (as in a geometric sequence). Instead, the height of the T-shirts changes in a non-linear way due to the effects of gravity over time, characterized by the quadratic formula.

### Summary:
- **Common Difference/Ratio**: Not applicable in this situation.
- **Y-Intercept**: \(2\) feet, representing the initial launch height of the T-shirts.
Answered by GPT-4o mini
### Common Difference or Ratio:
Not applicable; the motion follows a quadratic model, not a sequence.

### Y-Intercept:
- **Value**: 2 feet
- **Meaning**: This represents the initial height of the T-shirts when launched from the golf cart.
Answered by GPT-4o mini
To determine the type of sequence using an explicit formula, please provide the specific formula you are referencing.

### General Guidance:
- **Arithmetic Sequence**: If the formula is of the form \( a_n = a_1 + (n-1)d \), where \( d \) is a constant difference.
- **Geometric Sequence**: If the formula is of the form \( a_n = a_1 \cdot r^{(n-1)} \), where \( r \) is a constant ratio.

With the specific formula, I can help you identify the type of sequence!