GijrTfz0tIU An Arithmetic Sequence is made by adding the same value each time.
This sequence has a difference of 3 between each number.
This sequence has a difference of 5 between each number. The value added each time is called the "common difference" What is the common difference in this example?
The common difference could also be negative:
This common difference is −2 1739, 1740, 2511, 9771, 9772 nwazO55Bkzo A Geometric Sequence is made by multiplying by the same value each time.
This sequence has a factor of 3 between each number. What we multiply by each time is called the "common ratio". In the previous example the common ratio was 3: We can start with any number:
This sequence also has a common ratio of 3, but it starts with 2.
This sequence starts at 1 and has a common ratio of 2. The common ratio can be less than 1:
This sequence starts at 10 and has a common ratio of 0.5 (a half). But the common ratio can't be 0, as we get a sequence like 1, 0, 0, 0, 0, 0, 0, ... 658,796, 1741, 10006, 10007 There are also many special sequences, here are some of the most common: Triangular Numbers
This Triangular Number Sequence is generated from a pattern of dots that form a triangle. By adding another row of dots and counting all the dots we can find the next number of the sequence: Square Numbers
They are the squares of whole numbers: 0 (=0×0) 1 (=1×1) 4 (=2×2) 9 (=3×3) 16 (=4×4) etc... Cube Numbers
They are the cubes of the counting numbers (they start at 1): 1 (=1×1×1) 8 (=2×2×2) 27 (=3×3×3) 64 (=4×4×4) etc... Fibonacci Numbers
The Fibonacci Sequence is found by adding the two numbers before it together. The 2 is found by adding the two numbers before it (1+1) The 21 is found by adding the two numbers before it (8+13) The next number in the sequence above would be 55 (21+34) Can you figure out the next few numbers? Other SequencesThere are lots more! You might even think of your own ... 1736, 1737, 3860, 3861, 3862, 1735, 1738 Copyright © 2021 MathsIsFun.com |