Consider the Sequence Defined By $a _ { n } = \left( \frac { 2 } { 3 } \right) ^ { n }$

question 315

Essay

Consider the sequence defined by $a _ { n } = \left( \frac { 2 } { 3 } \right) ^ { n }$ . (n starts at 1)
(a) Write the first five terms of the sequence.(b) Determine the limit of the sequence.(c) Let $b _ { n } = \frac { a _ { n + 1 } } { a _ { n } }$ . Write the first five terms of this sequence.(d) Determine the limit of $b _ { n }$ .

---

Definitions:

Null Hypothesis

The hypothesis that predicts no relationship or effect between the independent and dependent variables being studied.

Alpha

Alpha, in statistics, is the threshold p-value that determines the critical level of significance at which the null hypothesis can be rejected, typically set at 0.05.

Null Hypothesis

A statement suggesting that there is no significant difference or effect, serving as a default position until proven otherwise.

Government's Definition

The specific meaning or interpretation of a term as provided by official government documentation or legislation.