SOLUTION: sequence50,15,40,59

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Question 1138736: sequence50,15,40,59
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

sequence 50,15,40,59+
first find differences to see what formula you need
50.......15.......40.......59
.....35.......25.......19
...........10.......6
.................4 ->3rd difference->you need
3rd degree function

a%5Bn%5D=an%5E3%2Bbn%5E2%2Bcn%2Bd
use given terms, set up system of four equations
a%5B1%5D=50, n=1
50=a%2A1%5E3%2Bb%2A1%5E2%2Bc%2A1%2Bd
50=a%2Bb%2Bc%2Bd........eq.1

a%5B2%5D=15, n=2
15=a%2A2%5E3%2Bb%2A2%5E2%2Bc%2A2%2Bd
15=8a%2B4b%2B2c%2Bd .......eq.2

a%5B3%5D=40, n=3
40=a%2A3%5E3%2Bb%2A3%5E2%2Bc%2A3%2Bd
40=27a%2B9b%2B3c%2Bd .......eq.3

a%5B4%5D=59, n=4
59=a%2A4%5E3%2Bb%2A4%5E2%2Bc%2A4%2Bd
59=64a%2B16b%2B4c%2Bd .......eq.4

solve the system:
50=a%2Bb%2Bc%2Bd........eq.1
15=8a%2B4b%2B2c%2Bd .......eq.2
40=27a%2B9b%2B3c%2Bd .......eq.3
59=64a%2B16b%2B4c%2Bd .......eq.4
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Solve the system of 4 equations using your favorite method.
In this example, the results are:
a+=+-11, b+=+96, c+=+-246, d+=+211
and your formula is:
a%5Bn%5D=-11n%5E3%2B96n%5E2-246n%2B211