would you guys be able to give me a hand with this problem solving question, i have no idea where to start...
Thanks
Zac
Hello, Zac!
Take the difference of consecutive pairs of terms.12. The first four tetrahedral numbers are: .
Find the pattern, then predict the next 3 terms of the sequence.
They are adding on consecutive "triangular" numbers.
. .
We will add on the next three triangular numbers:
. .
I'll skip all the algebra . . .What is the term of the sequence?
Hello, Zac!
This will take a while . . . better sit down.
Take differences of consecutive terms,
. . then take differences of the differences, and so on.
The third differences are constant.
. . This tells us that the generating fuction is a cubic.
The general cubic function is: .
We will use the first four terms of the sequence . . .
Substitute into [8]: .
Substitute into [5]: .
Substitute into [1]: .
Hence, the function is: .
. . Therefore: .