look at the differences between successive terms:
-1 -3 -5 -7
so, the next will be 15-9=6
the wonders of Wolfram
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
2a = -2
a = -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.
Answer this Question
math - patterns with fractions write a rule for the sequence.then,find the ...
4gr math - ...,450,470,480,__, __, __,... what are the nextthree numbers in this...
using patterns - I am having trouble working on number patterns. I have to find ...
Maths - I was given a question on number patterns. The queston states tha I must...
4th grade - Exploring Algebra: What's the rule? You can find patterns to figure ...
math - The Fibonacci sequence of numbers begins 1,1,2,3,5,8,13,21,34,55,…and ...
math...help please! - ok i REALLY am stumped. please help! it is a sequence ...
Math help please - 1. Each time a touchdown is scored in a football game, 6 ...
Algebra ll - Help please, I don't understand how to do this... Give an example ...
math - Three numbers in an arithmetic sequence sum to six. If you add 1 to the ...