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Question

There are 52 white keys on a piano. The frequency produced when a key is struck is the number of vibrations per second the key's string makes.

Describe the pattern in the relation.

Solution

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Answered 1 year ago
Answered 1 year ago
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Let us list down the sequence to see the pattern.

27.5, 55, 110, 220, 440, 880, 176027.5,\ 55,\ 110,\ 220,\ 440,\ 880,\ 1760

By observing the sequence, we can see that if we multiply the previous terms into 22 the answer will be the terms next to it.

27.5, 55×2, 110×2, 220×2, 440×2, 880×2, 1760×2\underbrace{27.5,\ 55}_{\times2}\underbrace{,\ 110}_{\times2}\underbrace{,\ 220}_{\times2}\underbrace{,\ 440}_{\times2}\underbrace{,\ 880}_{\times2}\underbrace{,\ 1760}_{\times2}

Therefore, our conjecture to the given sequence is "Multiply the previous term by 22".

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