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

question 301

Essay

Consider the sequence defined by $a _ { n } = \left( \frac { 3 } { 2 } \right) ^ { n }$ . (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 $b _ { n }$ .

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Definitions:

Aggregate Demand

The comprehensive market demand for all types of goods and services within an economy, pegged at a certain price level throughout a specific time period.

Future Generations

Refers to the people who will live in the future, whose interests are considered in various aspects of planning and policy-making, especially in environmental and sustainability contexts.

Keynesian Analysis

An economic approach that emphasizes the role of aggregate demand in influencing economic output and inflation.

Monetary Policy

The process by which a central bank or monetary authority controls the supply of money in an economy, often targeting interest rates to achieve economic objectives.