Question

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! :-)

Answer 1

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.