Arithmetic and Geometric Sequences
This section of Revision Maths explains arithmetic and geometric number sequences in algebra.
An arithmetic sequence is a sequence of numbers having a common first difference.
Taking the following sequence as an example
4 7 10 13 16
For any arithmetic sequence, the position to term formula is given by Un = dn + (a-d) where a is the first term and d is the common difference. So in the above example Un= 3n + (4-3), i.e. Un= 3n + 1.
The next number in the above sequence will therefore be U₆ = 3 x 6 + 1 = 19.
The video below explains number sequences and how to find the nth term.
In a geometric sequence you must multiply by a constant number (common ratio) r to go from one term to the next.
Taking the following example:
3 9 27 81 243
Each number is multiplied by 3 each time, giving us the common ratio of r = 3.
The term to term formula is Un₊₁ = 3Uₙ with U₁ = 3.
The position to term formula is Uₙ = 3ⁿ.
If we take the following example:
The common ratio r is ½
The term to term formula is Un ₊₁ = - un with U₁ = ½
The position to term formula is Uₙ = (-1/2)ⁿ