Write the Expression for the General (Or Nth)termrm $\mathbf { a } _ { \mathbf { n } } ,$

question 120

Multiple Choice

Write the expression for the general (or nth) termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence.
- $- \frac { 1 } { 3 } , - \frac { 1 } { 27 } , - \frac { 1 } { 243 } , - \frac { 1 } { 2187 } , \ldots$

• A) \(a _ { n } = \left( - \frac { 1 } { 3 } \right) ^ { n - 1 } + \frac { 8 } { 27 }\)
• B) \(a _ { n } = - \frac { 1 } { 3 } + \frac { 8 } { 27 } ( n - 1 )\)
• C) \(a _ { n } = - \frac { 1 } { 3 } + \frac { 1 } { 9 } ( n - 1 )\)
• D) \(a _ { n } = - \frac { 1 } { 3 } \left( \frac { 1 } { 9 } \right) ^ { n - 1 }\)

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Definitions:

T-Statistic

Re-defined: A value calculated from sample data during a t-test, used to assess the significance of the difference between two sample means.

α

Represents the level of significance in hypothesis testing, typically set at 0.05 or 5%.

P > .05

A statistical expression indicating that the probability of the observed data, or something more extreme, if the null hypothesis is true, is greater than 5%.

Null Hypothesis

The default assumption in statistical hypothesis testing that there is no significant effect or difference, intended to be challenged by the alternative hypothesis.