Download Patterns in Sequences

Patterns in Sequences
Number patterns
Sequences of numbers can have interesting patterns.
Here we list the most common patterns and how
they are made.
• Arithmetic
• Geometric
• Special Sequences
– Triangular Numbers
– Square Numbers
– Fibonacci Numbers
Arithmetic
• Sometimes you find the next number by
Adding the same number
3,7,11,15,?,?
Rule is previous number + 4 or n+4
n means number
Practice
9,17,25,?,?
n+8
5, 7.5,10,12.5,?,?
n+2.5
Geometric Sequences
Usually involves Multiplication
3, 6, 12, 24, ?
Previous number multiplied by 2
or n*2
or 2n
Practice
2, 6, 18, 54, ?, ?
n*3
Or 3n
162,486
Combination of Geometric and
Arithmetic
2, 5, 11, 23, ?, ?
47, 95
Previous number times 2 plus 1
Or 2n + 1
Practice
1, 6, 21, 66
3n + 3
2, 15, 41, 93
2n + 11
Triangular Numbers
Generated from a pattern of dots which
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
1, 4, 9, 16, 25, 36, 49, 64, 81, ...
The next number is made by squaring where
it is in the pattern.
The second number is 2 squared (22 or
2×2)
The seventh number is 7 squared (72 or
7×7) etc
Fibonacci Numbers
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
The next number is found by adding the two
numbers before it together.
The 2 is found by adding the two numbers in
front of it (1+1)
The 21 is found by adding the two numbers in
front of it (8+13)
What would then next number in the sequence
be?