Posted by **Cassie** on Monday, April 20, 2009 at 4:07pm.

The pattern is:

4, 8, 15, 25

Is the formula:

2.5n + 1.5n???

If you are wondering what the standard formula is, check my previous question.

Thank you! :-)

- Algebra -
**Reiny**, Monday, April 20, 2009 at 5:03pm
your formula can't be right,

try n=3 ---> 2.5(3) + 1.5(3) = 12 not the 15 that are needed.

I do these the following way:

4,8,15,25

the first set of differences between successive terms is 4,7,10

and the second differences are 3,3

so we have a constant difference in the second set, so the function must be quadratic

let it be y = an^2 + bn + c

from you data:

4 = a+b+c

8 = 4a+2b+c

15 = 9a+3b+c

subtract the first two: 4 = 3a + b

subtract the last two : 7 = 5a + b

now subract these two 3 = 2a

a = 3/2

sub into 4 = 3a+b --> b = -1/2

and finally back in the first gives us

c = 3

so y = (3/2)n^2 - n/2 + 3

try it, it works.

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