Write the First Four Terms of the Sequence Whose General $$a _ { n } = \frac { 3 ^ { n } } { ( n + 3 ) ! }$$

question 47

Multiple Choice

Write the first four terms of the sequence whose general term is given.
- $$a _ { n } = \frac { 3 ^ { n } } { ( n + 3 ) ! }$$

• A) \(\frac { 3 } { 4 } , \frac { 9 } { 5 } , \frac { 9 } { 2 } , \frac { 81 } { 7 }\)
• B) \(\frac { 1 } { 8 } , \frac { 3 } { 40 } , \frac { 3 } { 80 } , \frac { 9 } { 560 }\)
• C) \(\frac { 3 } { 7 } , \frac { 9 } { 8 } , 3 , \frac { 81 } { 10 }\)
• D) \(\frac { 1 } { 8 } , \frac { 3 } { 40 } , \frac { 3 } { 40 } , \frac { 9 } { 280 }\)

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Definitions:

REM Sleep

REM sleep, or Rapid Eye Movement sleep, is a unique phase of sleep characterized by rapid movements of the eyes, low muscle tone, and vivid dreams. It is considered critical for emotional regulation and memory consolidation.

Slow-Wave Sleep

A deep stage of sleep characterized by slow brain waves, where the body recovers and regenerates tissues, strengthens the immune system, and builds energy for the next day.

REM Sleep

A stage of sleep characterized by rapid eye movements, increased brain activity, vivid dreams, and temporary paralysis of the muscles.

Memory Consolidation

The process by which temporary, short-term memories are gradually converted into lasting, stable long-term memories.