Question

wabout the following number sequence?
8,5,4,9,1,7,6,10, 3, 2,0​

Answer 1

Answer:

The pattern 8 5 4 9 1 7 6 3 2 0 is an alphabetical pattern in which the numbers, when written out in letters, are listed in alphabetical order. The solution is found by listing the pattern as eight, five, four, nine, one, seven, six, three, two and zero.

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Answer 2

Answer:

The given sequence in the question is a type of finite sequence.

Step-by-step explanation:

• If a series contains a finite number of terms, it is finite; otherwise, it is infinite. Finite series: 4, 8, 12, 16,..., 64 The first number in the series is 4, and the final number is 64. The series is a finite sequence since it has a last term.

Every finite sequence with n terms can be fit by a polynomial with a degree of no more than (n -1). The fundamental notion is that, given a polynomial p:

$p(x) = a_n_-_1 x^n^-^1 + a_n_-_2x^n^-^2+$….$+ a_0$ and therefore a sequence forms which is $u_1, u_2,$….$u_3,$ then we get :

$p(1) = u_1, p(2) = u_2, p(n) =u_n$

is a linear system of n equations with n unknowns that has a single solution in all cases (because the n X n matrix that arises is a Vandermonde matrix).

If you carry out the aforementioned, you'll get the polynomial:

$p(x) = \frac{103}{30240} x^9 - \frac{1367}{8064} x^8 - \frac{4049}{1120}x^7 -\frac{8287}{192} x^6 - \frac{455219}{1440}x^5 -\frac{561667}{384}x^4 -\frac{128139587}{30240}x^3\\ \\-\frac{14772229}{2016}x^2 -\frac{5677843}{840} x^1 - 2475$

You may independently verify that p(1) = 8, p(2) = 5, p(3) = 10, and p(10) = 2.

Any finite sequence, including the one in question, has a pattern in this sense.

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