Mia spins two spinners. Each spinner has sections labeled A, B, and C. If each spinner lands in one of the lettered sections, wh
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Morse code is essentially the same as binary. That is, there are two "digits", a dot or a dash.
There are 26 letters in the English alphabet. Clearly, we can't just use one dot or dash, since that could only encode 2 letters at the most. We can't use two symbols because that could only encode 4 letters at the most. Similarly, 3 symbols means
letters at most.
We have to select the smallest power of 2 that exceeds or is equal to 26. In this case,
, so we would have to use up to 5 symbols to encode each letter in the alphabet.
There are 26 letters in the English alphabet. Clearly, we can't just use one dot or dash, since that could only encode 2 letters at the most. We can't use two symbols because that could only encode 4 letters at the most. Similarly, 3 symbols means
We have to select the smallest power of 2 that exceeds or is equal to 26. In this case,
Check the forward differences of the sequence.
If , then let
be the sequence of first-order differences of
. That is, for n ≥ 1,
so that .
Let be the sequence of differences of
,
and we see that this is a constant sequence, . In other words,
is an arithmetic sequence with common difference between terms of 2. That is,
and we can solve for in terms of
:
and so on down to
We solve for in the same way.
Then
and so on down to