0
U{n} = (-52n⁵ + 795n⁴ -4510n³ + 12045n² - 14518n + 6720)/120
Which gives U{1-5} = {4, 7, 13, 25, 49} and U6 = 42.
There are an infinite number of polynomials which will give the given sequence when the values 1-5 are input.
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What your teacher is most likely expecting is:
U{n} = 2.5 + 1.5 × (2ⁿ - 1)
or U{n} = (5 + 3 × (2ⁿ - 1)) / 2
Discovered via:
U2 = U1 + 3
U3 = U2 + 3 × 2
U4 = U3 + 3 × 2²
U{n} = U{n-1} + 3 × 2ⁿ⁻²
→ U1 = U0 + 3 × 2⁻¹
→ U0 = U1 - 3 × 2⁻¹
= 4 - 3/2
= 2.5
→ U1 = U0 + 3 × 2⁻¹ = 2.5 + 3 × 2⁻¹
U2 = U1 + 3 × 2⁰ = 2.5 + 3 × 2⁻¹ + 3 × 2⁰
U3 = U2 + 3 × 2¹ = 2.5 + 3 × 2⁻¹ + 3 × 2⁰ + 3 × 2¹
→ for n = 1, 2, 3, ...
U{n} = 2.5 + 3 × 2⁻¹ + 3 × 2⁰ + 3 × 2¹ + ... + 3 × 2ⁿ⁻²
= 2.5 + 3 × 2⁻¹ × (1 + 2¹ + 2² + ... + 2ⁿ⁻¹)
= 2.5 + 1.5 × (2ⁿ - 1)/(2 - 1)
= 2.5 + 1.5 × (2ⁿ - 1)
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Number of terms in the following arithmetic sequence 1 5 9 13 49?
Assuming the sequence does not merely skip from 13 to 49, and instead carries on in the same pattern, the sequence proceeds thus:1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49.This is thirteen terms. The formula for finding these terms is 4x-3.
What is the missing number in this sequence 1 9 25 81 100?
Ascending terms in the sequence are equal to 12, 32, 52, __, 92, and, for some reason, 102, not 112. Therefore, assuming the last term in the sequence to be 112 = 121, the fourth term in the sequence is 72 = 49.
What is next in the sequence 25 36 49 64?
81
Is the sequence 3-5-7-9-11-13-15 right as a sequence of square numbers go?
3-5-7-9-11-13-15 answer to1-4-9-16-25-36 what are the next 2 numbers and fill space between these which is what we come up with 3-5-7-9-16-25-36-49-64
What is the nth term if the sequence is 17 25 33 41 49?
The difference between successive terms is 8 tn = 8n + 9 or 8(n+1)+1 where n = 1,2,3,...
Number of terms in the following arithmetic sequence 1 5 9 13 49?
Assuming the sequence does not merely skip from 13 to 49, and instead carries on in the same pattern, the sequence proceeds thus:1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49.This is thirteen terms. The formula for finding these terms is 4x-3.
What is the missing number in this sequence 1 9 25 81 100?
Ascending terms in the sequence are equal to 12, 32, 52, __, 92, and, for some reason, 102, not 112. Therefore, assuming the last term in the sequence to be 112 = 121, the fourth term in the sequence is 72 = 49.
What is next in the sequence 25 36 49 64?
81
What is 13 over 49 in lowest term?
13/49 is in its lowest terms
Choose the next number in the sequence 25 49 81?
121.
What is the nth term for this sequence 4 7 13 22 34?
To find the nth term of a sequence, we first need to determine the pattern or rule that governs the sequence. In this case, the sequence appears to be increasing by adding consecutive odd numbers: 3, 6, 9, 12, and so on. Therefore, the nth term formula for this sequence is Tn = 3n^2 + n. So, the nth term for the sequence 4, 7, 13, 22, 34 is Tn = 3n^2 + n.
What is the nth term for the sequence 57 55 53 51?
(Term)n = 59 - 2n
Complete the sequence 100 81 64?
.... 49, 36, 25, 16, 9, 4 and 1
The missing squre numbers in this sequence 4 9 16 -- 36 ---?
They are 25 and 49
What is the nth term for 5 10 19 32 49 nth term?
To find the nth term of this sequence, we first need to identify the pattern. The differences between consecutive terms are 5, 9, 13, 17, and so on. These are increasing by 4 each time. This means that the nth term can be calculated using the formula n^2 + 4n + 1. So, the nth term for the sequence 5, 10, 19, 32, 49 is n^2 + 4n + 1.
What fraction is reducd to 1.96 in the lowest term?
49/25
Is the sequence 3-5-7-9-11-13-15 right as a sequence of square numbers go?
3-5-7-9-11-13-15 answer to1-4-9-16-25-36 what are the next 2 numbers and fill space between these which is what we come up with 3-5-7-9-16-25-36-49-64
