find 5 rational numbers between 3 and 4 using x(n+1)/n+1, y(n+1)/n+1
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Answer:
Therefore, five rational numbers between 3 and 4 are 7/2, 13/4, 25/8, 49/16 and 57/16.
Step-by-step explanation:
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Find the five rational numbers between 3 and 4.
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Hint: The rational number between a and b is (a+b)2, use this equation to find the rational numbers between the given two numbers. Rational numbers are the numbers which can be written as pq where p and q are integers and q≠0.
Complete step-by-step solution -
Given, to find 5 rational numbers between 3 and 4.
As, we know, the rational number between a and b is given by, (a+b)2
Hence, the rational number between 3 and 4 is (3+4)2=72=3.5
Rational number between 3 and 7/2 is ⎡⎣⎢⎢⎢3+(72)2⎤⎦⎥⎥⎥=134=3.25
Rational number between 3 and 13/4 is ⎡⎣⎢⎢⎢3+(134)2⎤⎦⎥⎥⎥=258=3.125
Rational number between 3 and 25/8 is ⎡⎣⎢⎢⎢3+(258)2⎤⎦⎥⎥⎥=4916=3.0625
Rational number between 25/8 and 2 is ⎡⎣⎢⎢⎢(258)+42⎤⎦⎥⎥⎥=5716=3.5625
✔verify answer
The rational number between a and b is (a+b)2, use this equation to find the rational numbers between the given two numbers. Rational numbers are the numbers which can be written as pq where p and q are integers and q≠0.
Complete step-by-step solution -
As, we know, the rational number between a and b is given by, (a+b)2
Hence, the rational number between 3 and 4 is (3+4)2=72=3.5
Rational number between 3 and 7/2 is ⎡⎣⎢⎢⎢3+(72)2⎤⎦⎥⎥⎥=134=3.25
Rational number between 3 and 13/4 is ⎡⎣⎢⎢⎢3+(134)2⎤⎦⎥⎥⎥=258=3.125
Rational number between 3 and 25/8 is ⎡⎣⎢⎢⎢3+(258)2⎤⎦⎥⎥⎥=4916=3.0625
Rational number between 25/8 and 2 is ⎡⎣⎢⎢⎢(258)+42⎤⎦⎥⎥⎥=5716=3.5625
Therefore, five rational numbers between 3 and 4 are 7/2, 13/4, 25/8, 49/16 and 57/16.
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