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Q: What number come number after 1 4 16?

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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

36

1 do

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

Square root of -1 is an imaginary number (√-1 = i), √-16 = √-1 * √16 √-16 = i * 4 √-16 = 4 i

1/16 ---------------------------------------------------- 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

The Pattern is 1^2- 2^2- 3^2- 4^2- 5^2 or 1 - 4 - 9 - 16 - 25 The next number in the series is 6^2 or 36

Let x be a number. 16=(3+x)*4 16=12+4x 16-12=12+4x-12 4=4x 4/4=4x/4 1=x Therefore a number is 1.

Take your number to the exponent (1/4). Example: Fourth root of 16. 16^ (1/4) = 2

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