SOLUTION: In exercises 1-6, construct a difference table to predict the next term of each sequence. 4.) 0, 10, 24, 56, 112, 190

Question 196447This question is from textbook
: In exercises 1-6, construct a difference table to predict the next term of each sequence.
4.) 0, 10, 24, 56, 112, 190 This question is from textbook

Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
x,,,,,,1,,,,,2,,,,3,,,,,,4,,,,,5,,,,,,6
.
f(x),,,,0,,,10,,,24...56,,,112,,,190,,,,,,,,base
.
d,,,,,,,,,,10,,,,14,,,32,,,56,,,78,,,,,,,,,,,,,1st degree
.
d,,,,,,,,,,,,,,,,,4,,,,,18,,,24,,,22,,,,,,,,,,,,,,2nd degree
.
d,,,,,,,,,,,,,,,,,,,,,14,,,,6,,,,,-2,,,,,,,,,,,,,,,,,3rd degree
.
d,,,,,,,,,,,,,,,,,,,,,,,,,,-8,,,,-8,,,,,,,,,,,,,,,,,,,4th degree
.
This defines f(x) = ax^4 +bx^3 + cx^2 + dx +e
.
(1) 0 = a(1)^4 +b(1)^3 +c(1)^2 +d(1)^1 +e
.
(2) 10 = a(2)^4 +b(2)^3 +c(2)^2 +d(2)^1 +e
.
(3) 24 = a(3)^4 +b(3)^3 +c(3)^2 +d(3)^1 +e
.
(4) 56 = a(4)^4 +b(4)^3 +c(4)^2 +d(4)^1 +e
.
(5) 112 =a(5)^4 +b(5)^3 +c(5)^2 +d(5)^1 +e
.
(6) 190 = a(6)^4 +b(6)^3 +c(6)^2 +d(6)^1 +e
.
now solving these simultaneously, using successive substitutions (and mult),
or matrix computation
.
Results in approx,,, f(x) = -.03 x^4 +1.49x^3 -7.32x^2 +21.93x-16.07
.
checking shows good agreement at low end, but about 70 % of actual at high end
.
making this correction,,,f(7) = 311 approx
.
Time does not permit any further computation, but perhaps this will give you a good start
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