Summary Number Patterns Study Notes

Number Patterns
MATHEMATICS GRADE 12
BY NIKITA VERMEULEN

, PATTERNS, SEQUENCES & SERIES
SEQUENCES

ARITHMETIC

A sequence in which the difference between any 2 consecutive terms is common

 Constant difference between any 2 consecutive terms  d=T n −T n−1
 General form: a+ ( a+d ) + ( a+ 2 d ) +¿ … ¿

Graph of the sequence lies on a straight line

Tn=a+( n−1)d

QUADRATIC

Common 2nd difference between any 2 consecutive terms

Graph of the sequence lies on a parabola

Tn=a n2 +bn+c
How to determine the expression

1. Determine the constant 2nd difference
2. Calculate a  2a = 2nd difference
3. Solve for b∧c by substitution in 2 terms & using simultaneous equations
4. Substitute all values into Tn=a n2 +bn+c

GEOMETRIC

Tn
 Constant ratio between any 2 consecutive terms  r =
Tn−1
2
 General form: a+ ar +a r +¿… ¿

Graph of the sequence lies on an exponential curve

Tn=a r n−1

SERIES

The sum of certain numbers of terms in a sequence

The notation used in series is an extension of the notation used in sequences


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