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Class 11
Mathematics
Sequence and Series
if nbsp is the a m between nbsp a nbsp and nbsp b...

Question:
If $fraction numerator a to the power of n plus b to the power of n over denominator a to the power of n minus 1 end exponent plus b to the power of n minus 1 end exponent end fraction$ is the A.M. between a and b, then find the value of n.

Answer:

A.M. of a and b = $fraction numerator a plus b over denominator 2 end fraction$

According to the given condition,

$fraction numerator a plus b over denominator 2 end fraction equals fraction numerator a to the power of n space space space end exponent plus space b to the power of n over denominator a to the power of n minus 1 end exponent plus b to the power of n minus 1 end exponent end fraction rightwards double arrow open parentheses a plus b close parentheses open parentheses a to the power of n minus 1 end exponent plus b to the power of n minus 1 end exponent close parentheses equals 2 open parentheses a to the power of n plus b to the power of n close parentheses rightwards double arrow a to the power of n plus a b to the power of n minus 1 end exponent plus b a to the power of n minus 1 end exponent plus b to the power of n equals 2 a to the power of n plus 2 b to the power of n rightwards double arrow a b to the power of n minus 1 end exponent plus a to the power of n minus 1 end exponent b equals a to the power of n plus b to the power of n rightwards double arrow a b to the power of n minus 1 end exponent minus b to the power of n equals a to the power of n minus a to the power of n minus 1 end exponent b rightwards double arrow b to the power of n minus 1 end exponent open parentheses a minus b close parentheses equals a to the power of n minus 1 end exponent open parentheses a minus b close parentheses rightwards double arrow b to the power of n minus 1 end exponent equals a to the power of n minus 1 end exponent rightwards double arrow open parentheses a over b close parentheses to the power of n minus 1 end exponent equals 1 equals open parentheses a over b close parentheses to the power of 0 rightwards double arrow n minus 1 equals 0 rightwards double arrow n equals 1$

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Question:
If $fraction numerator a to the power of n plus b to the power of n over denominator a to the power of n minus 1 end exponent plus b to the power of n minus 1 end exponent end fraction$ is the A.M. between a and b, then find the value of n.

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Question: If is the A.M. between a and b, then find the value of n.

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Question:
If $fraction numerator a to the power of n plus b to the power of n over denominator a to the power of n minus 1 end exponent plus b to the power of n minus 1 end exponent end fraction$ is the A.M. between a and b, then find the value of n.