Best Answer

1/16

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The above answer of 1/16 is the answer your teacher is more likely wanting as it makes the series so far a GP (Geometric Progression) with U{n} = 64 × (¼)ⁿ⁻¹. However, it is possible to find infinitely many polynomials which also give {64, 16, 4, 1, ¼} for the first five terms, but then diverge and continue the sequence in different ways, for example:

U{n} = (-153n⁵ + 3740n⁴ - 32735n³ + 131560n² - 246172n + 174480)/480

gives {64, 16, 4, 1, ¼} for n = {1, 2, 3, 4, 5}, so the next term U{6} = 42

U{n} = (27n⁴ - 414n³ + 2385n² - 6198n + 6248)/32

gives {64, 16, 4, 1, ¼} for n = {1, 2, 3, 4, 5}, so the next term U{6} = 15¼

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1/4

Q: Which number should come next 64 16 4 1?

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7

It appears that they are increasing by odd numbers of 3 5 7 So the next number should be 16+9 = 25

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This is the series of square numbers, (16= 4*4). The next number is 5*5=25.

If the numbers are 64 16 4 1 and 1/4 then the next number is 1/16 because each number is being divided by 4

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The next number in the sequence is... 64

The next number is 25 but there are the sequence is infinite so there can be no end to the sequence.

It is 128 because they are doubled up each time

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36...49....64...81...100...121...144 They are the square numbers.