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Which number should come next 64 16 4 1 ¼?

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1/16

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The above answer of 1/16 is the answer your teacher is more likelywanting as it makes the series so far a GP (Geometric Progression)with U{n}=64 × (¼)ⁿ⁻¹. However, it is possible to find infinitelymany polynomials which also give {64, 16, 4, 1, ¼} for the firstfive terms, but then diverge and continue the sequence in differentways, 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 termU{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 termU{6}=15¼
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What number should come next in this series 1 4 9 16?

The series appears to increase as follows: 1 (+3), 4 (+5), 9 (+7), 16,, etc. If so, the next number in the series would be 25 (16 + 9). * * * * * While mathematically equi

What is the next number in the sequence 1 4 16 64?

The sequence is a geometric progression . Here, first term(a)=1 and common multiple(r)=4. nth term of G.P. is given by a n=ar n-1 If we put n=5, then a 5=1x