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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
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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.
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t(n) = 12*n + 5
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Which is the term number when the term value is 53?
To find the term number when the term value is 53 in a sequence, you need to know the pattern or formula of the sequence. If it is an arithmetic sequence with a common difference of d, you can use the formula for the nth term of an arithmetic sequence: ( a_n = a_1 + (n-1)d ), where ( a_n ) is the nth term, ( a_1 ) is the first term, and d is the common difference. By plugging in the values, you can solve for the term number.
