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),

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where a is the first term, d is the difference between the first and second terms and c is the second difference.


  1. 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'.
  2. In the next column of your table write the differences between the term of 'n2' and your sequence.
  3. Find the formula for this new sequence using dn + (a - d)
  4. 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