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Provide an Appropriate Response {rn}\left\{ \mathrm { r } _ { \mathrm { n } } \right\}

question 50

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Provide an appropriate response.
-A sequence of rational numbers {rn}\left\{ \mathrm { r } _ { \mathrm { n } } \right\} is defined byr1=21b \mathrm { y } \mathrm {} \mathrm { r } _ { 1 } = \frac { 2 } { 1 } , and if rn=ab\mathrm { r } _ { \mathrm { n } } = \frac { \mathrm { a } } { \mathrm { b } } then rn+1=a+bab\mathrm { r } _ { \mathrm { n } } + 1 = \frac { \mathrm { a } + \mathrm { b } } { \mathrm { a } - \mathrm { b } } . Find r50\mathrm { r } _ { 50 } .


Definitions:

Sensitization

An increased response to a stimulus after repeated exposure, often leading to heightened sensitivity.

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Sites where neurons communicate with each other or with effector organs through chemical messengers.

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Specialized junctions between cells that allow for the direct passage of ions and electrical signals, facilitating rapid communication.

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