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What is the fourth difference sequence formula?

Anonymous

∙ 12y ago

Updated: 4/28/2022

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

Wiki User

∙ 12y ago

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