Math
posted by Aiden on .
Good day please help.Iam struggling with number patterns,i must fid the rule and also give the nextthree numbers in the sequence.
31;30;27,22;15

look at the differences between successive terms:
1 3 5 7
so, the next will be 159=6 
the wonders of Wolfram
http://www.wolframalpha.com/input/?i=pattern+%2831%2C30%2C27%2C22%2C15%29
actual work
did you notice that consecutive differences are
1, 3, 5, 7 ?
this forms an arithmetic sequence, so a quadratic will act as the defining function.
let the sequence be defined by
f(n) = an^2 + bn + c
for (1,31) > a + b + c = 31 , #1
for (2,30) > 4a + 2b + c = 30 , #2
subtract these two equations
3a + b = 1
for (3,27) > 9a + 3b + c = 27 , #3
#3  #2 > 5a + b = 3
5a + b = 3
3a + b = 1
subtract:
2a = 2
a = 1
in 3a+b=1
3 +b = 1
b = 2
in #1: a+b+c=31
1+2+c = 31
c = 30
the defining function is
fn) = n^2 + 2n + 30
(just like Wolfram said) 
I guess I didn't read the question too carefully, and failed to answer it fully.