IEB GRADE 12 PATTERNS SUMMARY

Patterns Revision Summary

Sequences and Series

Arithmetic Sequence or Linear Pattern with a constant 1st difference
n
d T2  T1 T3  T2 Tn a  (n  1)d Sn  (2a  (n  1)d )
2
Geometric Sequence or Exponential Pattern with a constant ratio
T2 T3 a (1  r n ) a
r  n 1 Sn  S  if  1  r  1
T1 T2 Tn a.r 1 r 1 r

Sigma Notation: Used for the sum of a series
Recognize the different forms for an AP and a GP
20 20
k 1
 2k  4  4.2
k 1 is an AP k 1 is a GP
2
Quadratic Pattern: Tn an  bn  c

2a= 2nd Difference 3a +b = The first 1st difference a + b + c = 1st term

Always write out the pattern and show at least four 1st differences and three 2nd
differences

Combined Patterns:

Every alternate term (odd and even terms) form 2 different series

The sum to 100 terms would be the sum to 50 terms of each series

Types of Questions:

1) Given the first 3 terms enables you to find a and either d or r and any Tn or Sn
2) Given 2 terms enables you to find the sequence by solving simultaneous equations
3) Given a term or the sum and either a or d (or r) enables you to find n, the term
number or number of terms in the sum.
4) To find for which values of x a geometric series converges, make  1  r  1
where r is written in terms of x and solve for x

Remember : GP’s use exponents and logs and AP’s use linear and quadratic questions