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 15-9=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.
Good day! I can definitely help you with number patterns. Let's analyze the given sequence: 31, 30, 27, 22, 15.
To find the rule or pattern in a number sequence, we need to examine the differences between consecutive terms.
Let's calculate the differences between each term in the sequence:
30 - 31 = -1
27 - 30 = -3
22 - 27 = -5
15 - 22 = -7
By looking at these differences, we can observe that they are decreasing by 2 each time. This suggests that the sequence follows a decreasing pattern.
Now, to find the next three numbers in the sequence, we can continue this pattern of decreasing differences:
15 - 7 = 8
8 - 9 = -1
Therefore, the next three numbers in the sequence would be: 8, -1, -8.
To summarize, the rule or pattern in the given sequence is that each term is obtained by subtracting a decreasing odd number. The next three numbers in the sequence are 8, -1, and -8.