Question

The formula for the nth term of the sequence 2, 15, 48,110,210, ...
n(n+1)(3n-1)
is
2
Find the 9th term.​

Answer 1

Answer:

know the pattern rule, but for you that don’t know, this is how it is done.

Find the first differences to see if they are the same:

3, 5, 7, 9

Find the second differences to see if they are the same:

2, 2, 2

Since the second differences are the same, this is a quadratic function. As you can see, you can square the term number and subtract 1, 4, 9, 16, 25 are the square numbers of 1, 2, 3, 4 and 5. Subtract 1 from each one of them: 0, 3, 8, 15, 24.

n^2–1 would be the nth term