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.

Answer 1

20-3=17
17-4=13
13-5=8
8-6=2

Answer 2

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