Find The $n ^ { \text {ct } }$ Term of the Sequence Whose First Several Terms Are

question 98

Multiple Choice

Find the $n ^ { \text {ct } }$ term of the sequence whose first several terms are $\frac { 1 } { 4 } , - \frac { 1 } { 9 } , \frac { 1 } { 16 } , - \frac { 1 } { 25 } , \ldots$

• A) \(Q _ { n } = \frac { ( - 1 ) ^ { n + 1 } } { n ^ { 2 } }\)
• B) \(a _ { n } = \frac { ( - 1 ) ^ { n + 1 } } { ( n + 1 ) ^ { 2 } }\)
• C) \(a _ { \mathrm { n } } = \frac { ( n + 1 ) ^ { n } } { 4 ^ { 2 } }\)
• D) \(a _ { n } = \frac { ( 1 ) ^ { n } } { ( 2 n ) ^ { 2 } }\)
• E) none of these

---

Definitions:

Alpha Motor Neurons

Nerve cells that innervate muscle fibers, responsible for initiating muscle contraction.

Muscle Spindle

A sensory receptor located in muscles that senses changes in muscle length and contributes to the control of muscle contraction.

Afferent Neurons

Nerve cells that carry sensory information from the body's periphery to the central nervous system.

Stretch Reflex

A muscle contraction in response to stretching within the muscle, serving as a protective mechanism to prevent overstretching.