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A solution for 4th difference sequence is:
Formula: Tn = an4+ bn3+ cn2 + dn + e
1st term = a + b + c + d + e
1st difference = 15a + 7b + 3c + d
2nd difference = 50a + 12b + 2c
3rd difference = 60a + 6b
4th difference = 24a
Example:
Tn (term number) = 1 2 3 4 5 6 7
Sequence = 1 41 209 643 1529 3101 5641
1st difference = 40 168 434 886 1572 2540
2nd difference = 128 266 452 686 968
3rd difference = 138 186 234 282
4th difference = 48 48 48
Step 1: 4th difference = 24a:
24a = 48
a = 2
Step 2: 3rd difference = 60a + 6b:
60(2) + 6b = 138
b = 3
Step 3: 2nd difference = 50a + 12b + 2c:
50(2) + 12(3) + 2c = 128
c = -4
Step 4: 1st difference = 15a + 7b + 3c + d:
15(2) + 7(3) + 3(-4) + d = 40
d = 1
Step 5: 1st 1st term = a + b + c + d + e:
2 + 3 - 4 + 1 + e = 1
e = -1
Answer:
Tn = 2n4+ 3n3- 4n2 + n - 1
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A sequence has nth term formula 3n+5. What is the fourth term?
8
How do you find out the formula for a Quadratic Sequence?
A quadratic sequence is when the difference between two terms changes each step. To find the formula for a quadratic sequence, one must first find the difference between the consecutive terms. Then a second difference must be found by finding the difference between the first consecutive differences.
A certain arithmetic sequence has the recursive formula If the common difference between the terms of the sequence is -11 what term follows the term that has the value 11?
In this case, 22 would have the value of 11.
The simple formula for the nth term of an arithmetic sequence is an equals 4n plus 16 What is the explicit formula corresponding to the simple formula?
The explicit formula for an arithmetic sequence is given by an = a1 + (n-1)d, where a1 is the first term and d is the common difference. In this case, the first term a1 is 16, and the common difference d is 4. Therefore, the explicit formula for the arithmetic sequence is an = 16 + 4(n-1) = 4n + 12.
What is a sequence in which a common difference separates terms?
arithmetic sequence
What is the difference between a geometric sequence and a recursive formula?
what is the recursive formula for this geometric sequence?
A sequence has nth term formula 3n+5. What is the fourth term?
8
How do you find out the formula for a Quadratic Sequence?
A quadratic sequence is when the difference between two terms changes each step. To find the formula for a quadratic sequence, one must first find the difference between the consecutive terms. Then a second difference must be found by finding the difference between the first consecutive differences.
Is one one fourth one seventh one tenth a arithemtic sequence?
An arithmetic sequence is a sequence of numbers where the difference is constant. The difference between 1 and 1/4 is 3/4. The difference between 1/4 and 1/7 is 3/28. The difference between 1/7 and 1/10 is 3/70. These differences are not constant.
How is a arithmetic sequence found?
You take the difference between the second and first numbers.Then take the difference between the third and second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Take the difference between the fourth and third second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Keep checking until you think the differences are all the same.That being the case it is an arithmetic sequence.If you have a position to value rule that is linear then it is an arithmetic sequence.
Does Every sequence have a formula associated with it?
no not every sequence has a formula associated with it.
What is the formula for the sequence 3-7-11-15-19?
Since the difference between each term is '4' , then the first part of the formula is '4n'.
How do you find the nth term in a sequence?
Finding the nth term is much simpler than it seems. For example, say you had the sequence: 1,4,7,10,13,16 Sequence 1 First we find the difference between the numbers. 1 (3) 4 (3) 7 (3) 10 (3) 13 (3) 16 The difference is the same: 3. So the start of are formula will be 3n. If it was 3n, the sequence would be 3,6,9,12,15,18 Sequence 2 But this is not our sequence. Notice that each number on sequence 2 is 2 more than sequence 1. this means are final formula will be: 3n+1 Test it out, it works!
How do you create a sequence in which 1 and one fourth is added to each number?
To form a linear (or arithmetic) sequence you need two things: a starting value and the common difference. You have provided the common difference but not the starting value. If the starting value was a, then the nth term in the sequence would beT(n) = a + 5/4*(n - 1).
A certain arithmetic sequence has the recursive formula If the common difference between the terms of the sequence is -11 what term follows the term that has the value 11?
In this case, 22 would have the value of 11.
What is the nth term for 1 7 13 19?
The given sequence is an arithmetic sequence with a common difference of 6. To find the nth term of this sequence, we can use the following formula: nth term = first term + (n - 1) x common difference where n is the position of the term we want to find. In this sequence, the first term is 1 and the common difference is 6. Substituting these values into the formula, we get: nth term = 1 + (n - 1) x 6 nth term = 1 + 6n - 6 nth term = 6n - 5 Therefore, the nth term of the sequence 1, 7, 13, 19 is given by the formula 6n - 5.
The simple formula for the nth term of an arithmetic sequence is an equals 4n plus 16 What is the explicit formula corresponding to the simple formula?
The explicit formula for an arithmetic sequence is given by an = a1 + (n-1)d, where a1 is the first term and d is the common difference. In this case, the first term a1 is 16, and the common difference d is 4. Therefore, the explicit formula for the arithmetic sequence is an = 16 + 4(n-1) = 4n + 12.
