Write the First Five Terms of the Sequence Defined Recursively $a _ { 1 } = - 8 , a _ { k + 1 } = - 3 a _ { k }$

question 92

Multiple Choice

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1.) $a _ { 1 } = - 8 , a _ { k + 1 } = - 3 a _ { k }$

• A) \(a _ { k } = ( 24 ) ^ { n } ; - 8 , - 512,4096 , - 32768,262144\)
• B) \(a _ { n } = - 8 ( - 3 ) ^ { n - 1 } ; - 8,24 , - 72,216 , - 648\)
• C) \(a _ { n } = - 8 n ; - 8 , - 16 , - 24 , - 32 , - 40\)
• D) \(a _ { k } = ( 24 ) ^ { n - 1 } ; - 8 , - 512,4096 , - 32768,262144\)
• E) \(a _ { n } = - 8 ( - 3 ) ^ { n } ; 24 , - 72,216 , - 648,1944\)

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Definitions:

Positive Self-esteem

The feeling of holding oneself in high regard, characterized by confidence and satisfaction in one's own abilities and worth.

Defensive Self-esteem

A form of self-esteem that is fragile and dependent on external validation or success.

Self-serving Bias

The common tendency to attribute one's successes to personal characteristics and failures to external factors.

Defensive Self-esteem

A fragile form of self-respect that is highly sensitive to criticism and failures, often leading to a defensive stance to protect one's self-image.