Write the First Five Terms of the Sequence $\left( - \frac { 1 } { 4 } \right) ^ { n + 2 }$

question 89

Multiple Choice

Write the first five terms of the sequence $\left( - \frac { 1 } { 4 } \right) ^ { n + 2 }$ . Assume that n begins with 1.

• A) \(a _ { 1 } = - \frac { 1 } { 64 } , a _ { 2 } = \frac { 1 } { 256 } , a _ { 3 } = - \frac { 1 } { 1024 } , a _ { 4 } = \frac { 1 } { 4096 } , a _ { 5 } = - \frac { 1 } { 16384 }\)
• B) \(a _ { 1 } = \frac { 1 } { 16 } , a _ { 2 } = \frac { 1 } { 64 } , a _ { 3 } = \frac { 1 } { 256 } , a _ { 4 } = \frac { 1 } { 1024 } , a _ { 5 } = \frac { 1 } { 4096 }\)
• C) \(a _ { 1 } = - \frac { 1 } { 16 } , a _ { 2 } = \frac { 1 } { 64 } , a _ { 3 } = - \frac { 1 } { 256 } , a _ { 4 } = \frac { 1 } { 1024 } , a _ { 5 } = - \frac { 1 } { 4096 }\)
• D) \(a _ { 1 } = \frac { 1 } { 16 } , a _ { 2 } = - \frac { 1 } { 64 } , a _ { 3 } = \frac { 1 } { 256 } , a _ { 4 } = - \frac { 1 } { 1024 } , a _ { 5 } = \frac { 1 } { 4096 }\)
• E) \(a _ { 1 } = \frac { 1 } { 64 } , a _ { 2 } = \frac { 1 } { 256 } , a _ { 3 } = \frac { 1 } { 1024 } , a _ { 4 } = \frac { 1 } { 4096 } , a _ { 5 } = \frac { 1 } { 16384 }\)

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Definitions:

Optimists

Individuals who tend to maintain a hopeful and positive outlook on life and its future outcomes, often facing challenges and setbacks with a sense of opportunity.

Explanatory Styles

Cognitive approaches individuals use to explain the causes of events, often categorized as optimistic or pessimistic.

Pessimists

Individuals who tend to see the worst aspect of things or believe that the worst will happen; a lack of hope or confidence in the future.

Stressful Life Experiences

Events or situations that cause significant stress or distress, impacting an individual's psychological and physical well-being.