Name: jason
Who is asking: Other
Level: All
Question:
1 4 10 20 35 56 84
what is the nth term
Hi Jason,
The difference method will work well here: form successive rows where the first row is your original sequence, and the k-th term in the next row is always the difference between the (k+1)-th term and the k-th term in the previous row:
1-st row: 1, 4, 10, 20, 35, 56, 84, ...
2-nd row: 3, 6, 10, 15, 21, 28, ...
3-rd row: 3, 4, 5, 6, 7, ...
4-th row: 1, 1, 1, 1, ...
If you can guess the 5-th term in the 4-th row, it will help you find the 6-th term in the 3-rd row, which will help you find the 7-th term in the 2-nd row, which will help you find the 8-th term in the first row.
You can then start over a few times, finding the next term in each sequence; after that, you will need to try to find a general expressions for the n-th term in each row.
Claude