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January 29, 2015

January 29, 2015

Posted by **Aiden** on Tuesday, July 22, 2014 at 12:13pm.

31;30;27,22;15

- Math -
**Steve**, Tuesday, July 22, 2014 at 12:20pmlook at the differences between successive terms:

-1 -3 -5 -7

so, the next will be 15-9=6

- Math -
**Reiny**, Tuesday, July 22, 2014 at 12:29pmthe 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)

- Math - thanks Reiny -
**Steve**, Tuesday, July 22, 2014 at 7:38pmI guess I didn't read the question too carefully, and failed to answer it fully.

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