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Standard XII

Mathematics

Distance Formula

The value of ...

Question

The value of a for which side of nth square equals the diagonals of $(n + 1)^{t h}$ square is

1/3

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1/4

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1/2

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1 \sqrt{2}

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Solution

The correct option is D $1 \sqrt{2}$
Given $(D i a g o n a l)_{n + 1} = (S i d e)_{n} \sqrt{2} a_{1} r^{n} = a_{1} r^{n - 1} \sqrt{2} r = 1 r = \frac{1}{\sqrt{2}}$

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The value of a for which side of nth square equals the diagonals of (n+1)th square is

The correct option is D 1√2Given (Diagonal)n+1=(Side)n√2a1rn=a1rn−1√2r=1r=1√2

The value of a for which side of nth square equals the diagonals of $(n + 1)^{t h}$ square is

The correct option is D $1 \sqrt{2}$
Given $(D i a g o n a l)_{n + 1} = (S i d e)_{n} \sqrt{2} a_{1} r^{n} = a_{1} r^{n - 1} \sqrt{2} r = 1 r = \frac{1}{\sqrt{2}}$