S-Cool Revision Summary
S-Cool Revision Summary
nth term
nth term = dn + (a - d)
where d is the difference and a is the first term.
If the second difference is constant (and first difference changes),
where a is the first term, d is the difference between the first and second terms and c is the second difference.
Alternatively:
- If the first difference keeps changing but the second difference is constant then the formula is something to do with 'n2'. Make a table showing the first few terms of 'n2'.
- In the next column of your table write the differences between the term of 'n2' and your sequence.
- Find the formula for this new sequence using dn + (a - d)
- Add it on to n2 to give you your final formula
Well-known sequences
Sequence | Name | nth term |
2,4,6,8,... | Even numbers | 2n |
1,3,5,7,... | Odd numbers | 2n - 1 |
1,4,9,16,25,... | Square numbers | n2 |
1,8,27,64,125,... | Cube numbers | n3 |
1,3,6,10,15,... | Triange numbers | ½ n(n + 1) |
2,3,5,7,11,13,... | Prime numbers | Not known |
1,1,2,3,5,8,13,... | Fibonacci numbers | Not needed |