0
There are an infinite number of possible answers - there are an infinite number of formulae that can be found to give t{1..5} = {12, 59, 294, 1469, 7344} which will give different values for t8.
eg:
t{n} = (376n⁴ - 3384n³ + 11186n² - 15369n + 7227)/3
gives t{1..5} = {12, 59, 294, 1469, 7344}, and t8 = 135889.
t{n} = (-4929n⁵ + 76943n⁴ - 446037n³ +1198513n² -1473498n + 649296)/24
also gives t{1..5} = {12, 59, 294, 1469, 7344}, but t8 = -381656.
However, the solution your teacher is probably expecting is based on the fact that:
U1 = 12
U{n} = 5U{n-1} - 1 for n ≥ 2
This leads to:
t1 = 12
t{n} = 12 + 47 × 5ⁿ⁻² for n ≥ 2
→ t8 = 917969
According to Wittgenstein's Finite Rule Paradox every finite sequence of numbers can be a described in infinitely many ways and so can be continued any of these ways - some simple, some complicated but all equally valid. Conversely, it is possible to find a rule such that any number of your choice can be the next one.
One possible solution can be obtained by fitting a polynomial of order 4.
Un = (376*n4 - 3384*n3 + 1186*n2 - 15369*n + 7227)/3 for n = 1, 2, 3, ...
which would give U8 = 135889.
Add your answer:
Earn +20 pts
What is the 8th term in the pattern 12 59 294 1469 7344?
It is 917969.
If the nth term of a sequence is 12n - 6 what is the 8th term?
90
What is the 8th term of the sequence 1 4 9 16 25?
The given sequence is the sequence of perfect squares starting from 1. The nth term of this sequence can be represented as n^2. Therefore, the 8th term would be 8^2, which equals 64. So, the 8th term of the sequence 1, 4, 9, 16, 25 is 64.
What is the 8th term in the Fibonacci sequence?
It is: 1 1 2 3 5 8 13 and 21 which is the 8th term
What is the 8th term of a sequence when the rule is 3n plus 4?
To find the 8th term of the sequence with the rule 3n + 4, you would substitute n = 8 into the formula. This gives you 3(8) + 4 = 24 + 4 = 28. Therefore, the 8th term of the sequence is 28.
What is the 8th term in the pattern 12 59 294 1469 7344?
It is 917969.
What is the 8th term for 12 59 294 1469 7344?
Any number that you choose can be the eighth term. It is easy to find a rule based on a polynomial of order 5 such that the first five numbers are as listed in the question followed by the chosen number in eighth position. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.The simplest answer, based on the following polynomial of order 4 U(n) = (376*n^4 - 3384*n^3 + 11186*n^2 - 15369*n + 7227)/3 for n = 1, 2, 3, ...gives U(8) = 135889.
How many days from 12th march 2011 until 8th october 2011?
294
How do you do nth term?
If you have this series: 1,2,3,4,5,6,7,8The 8th term is 8 and the n-th term is n.But if you have this series: 2,4,6,8,10,12,14,16The 8th term is 16 and the n-th term is 2n
If the nth term of a sequence is 12n - 6 what is the 8th term?
90
What is the 8th term of the sequence 1 4 9 16 25?
The given sequence is the sequence of perfect squares starting from 1. The nth term of this sequence can be represented as n^2. Therefore, the 8th term would be 8^2, which equals 64. So, the 8th term of the sequence 1, 4, 9, 16, 25 is 64.
What is the 8th term in the Fibonacci sequence?
It is: 1 1 2 3 5 8 13 and 21 which is the 8th term
If the nth term of a sequence is 12n-6 what is the 8th term?
90
Convert 0.125 to the lowest term?
1/8th
What is the value of the 8th term of the sequence 6?
48
What is the 8th term of a sequence when the rule is 3n plus 4?
To find the 8th term of the sequence with the rule 3n + 4, you would substitute n = 8 into the formula. This gives you 3(8) + 4 = 24 + 4 = 28. Therefore, the 8th term of the sequence is 28.
What is the 8th term of a series which is a geometric progression having 2nd term of -3 and a 5th term of 81?
the answer for the above question is -2187
