Find the Nth Term $a _ { n }$ Of a Sequence Whose First Four Terms Are Given

question 263

Multiple Choice

Find the nth term $a _ { n }$ of a sequence whose first four terms are given.
- $\frac { 1 \cdot 2 \cdot 3 \cdot 4 } { 2 } , \frac { 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 } { 4 } , \frac { 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 } { 6 } , \frac { 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 } { 8 } , \ldots$

• A) \(a _ { n } = \frac { ( n + 4 ) ! } { 2 ^ { n } }\)
• B) \(a _ { n } = \frac { ( n + 4 ) ! } { 2 n }\)
• C) \(a _ { n } = \frac { ( n + 3 ) ! } { 2 n }\)
• D) \(a _ { n } = \frac { ( n + 3 ) ! } { 2 ^ { n } }\)

---

Definitions:

Dependent Variable

The variable in a study or experiment that is expected to change or respond due to manipulation of the independent variable(s).

Graph

A visual representation of data designed to show relationships between sets of variables using points, lines, bars, or sections.

Straight Line

The shortest distance between two points, often used to describe a linear relationship in mathematics and physics.

Sample Regression Equation

A formula that estimates the relationship between variables using data from a sample, predicting the dependent variable based on independent variables.