Question
What is the rule for the sequence 20, 17, 13, 8, 2? I've been trying to answer it by second difference method but still don't get correct formula.
Answers
Vasantha
20-3=17
17-4=13
13-5=8
8-6=2
17-4=13
13-5=8
8-6=2
Reiny
the second differences are a constant so the relationship is quadratic.
the the equation be
y = ax^2 + bx + c
when x = 1
a+b+c = 20
when x=2
4a+2b+c = 17
when x = 3
9a+3b+c = 13
subtract 1str from 2nd
3a+b=-3
subtract 2nd from 3rd
5a + b = -4
now subtract those last two:
2a = -1
a = -1/2
in 3a+b=-3
-3/2 + b = -3
b = -3/2
in the 1st
-1/2 - 3/2 + c = 20
c = 22
y or f(x) = (-1/2)x^2 - (3/2)x + 22
or (-x^2 - 3x + 44)/2
the the equation be
y = ax^2 + bx + c
when x = 1
a+b+c = 20
when x=2
4a+2b+c = 17
when x = 3
9a+3b+c = 13
subtract 1str from 2nd
3a+b=-3
subtract 2nd from 3rd
5a + b = -4
now subtract those last two:
2a = -1
a = -1/2
in 3a+b=-3
-3/2 + b = -3
b = -3/2
in the 1st
-1/2 - 3/2 + c = 20
c = 22
y or f(x) = (-1/2)x^2 - (3/2)x + 22
or (-x^2 - 3x + 44)/2