Find a Formula for the General Term $a _ { n }$

question 129

Multiple Choice

Find a formula for the general term $a _ { n }$ of the sequence $\left\{ 1 , - \frac { 12 } { 10 } , \frac { 19 } { 15 } , - \frac { 26 } { 20 } , \frac { 33 } { 25 } , \ldots \right\}$ .

• A) \(\frac { ( - 1 ) ^ { n - 1 } ( 5 + 7 n ) } { 5 ( n + 1 ) }\)
• B) \(\frac { ( - 1 ) ^ { n } ( 5 + 7 n ) } { 5 n }\)
• C) \(\frac { ( 5 + 7 n ) } { 5 ( n + 1 ) }\)
• D) \(\frac { ( - 1 ) ^ { n } ( 5 - 7 n ) } { 5 ( n + 1 ) }\)
• E) \(\frac { ( - 1 ) ^ { n } ( 5 + 7 n ) } { ( n + 1 ) }\)
• F) \(\frac { ( - 1 ) ^ { n + 1 } ( 5 - 7 n ) } { 5 ( n + 1 ) }\)
• G) \(\frac { ( - 1 ) ^ { n } ( 5 + 7 n ) } { 5 ( n + 1 ) }\)
• H)None of these

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Definitions:

External Locus

An external locus of control refers to the belief that outside forces, beyond an individual's control, significantly influence life events and outcomes.

Secure Self-Esteem

A form of self-esteem characterized by a stable, positive self-image and confidence that is not overly reliant on external validation.

Positive Psychology

A branch of psychology focused on the study and enhancement of positive human functions, such as happiness and well-being.

Approval of Others

The act of seeking validation, acceptance, or endorsement from people around us.