MATHEMATICS
SUMMARY
PAPER 1 SUMMARY BOOK
Complied by Mr. Mangala
GRADE 11 & 12
Number Patterns and Series
Mathematics
A number pattern is a sequence of numbers that follows a specific rule where each term is
determined by a consistent operation applied to the previous term. They help us to identify and
describe relationships between numbers and solve problems.
Arithmetic Sequence
Number Pattern Language
An ARITHMETIC sequence is sequence of numbers
Sum(S): results of adding two or more terms of
in which the difference between consecutive terms
a sequence. is constant (same difference).
Product: results of multiplying two or more
Example
terms of a sequence.
Given the set of numbers: 2;5;8;11;14 …
Consecutive terms: terms that follows each
Difference (d) is 3
other in a sequence.
NEXT TERM is 17 (adding 3 to the PREVIOUS
Series: addition of all terms of a sequence. TERM)
Convergence: Series that come to one value
General term
(Geometric) where −𝟏 < 𝐫 < 𝟏.
Divergence: Series that continue expands. 𝐓𝐧 = 𝐚 + ሺ𝐧 − 𝟏ሻ𝐝
Where:
a – is the 1st term of sequence
Types of Number Patterns
d – constant difference
Arithmetic pattern
𝐓𝐧 – is the last term of sequence
𝒏 - is the position of term
Therefore: 𝒅
Geometric Pattern
= 𝑻𝒏 − 𝑻𝒏−𝟏
Lesson Objectives Multiple difference: 𝐓𝐧 − 𝐓𝐦 = ሺ𝐧 − 𝐦ሻ𝐝
n > m Restriction
Revision Arithmetic Sequence
Sum of Arithmetic Sequence Example
Relationship between Sn and Tn
Sigma Notation
REMEMBER!
1|P age
Multiple difference
𝐓𝟏 𝐓𝟐 𝐓𝟑 𝐓𝟒 𝐓𝟓 ; … … … 𝐓𝐧
𝑑 𝑑 𝑑 𝑑
Common differences
❖ 𝐓𝟐 − 𝐓𝟏 = 𝐝
❖ 𝐓𝟒 − 𝐓𝟏 = 𝟑𝐝
❖ 𝐓𝟓 − 𝐓𝟏 = 𝟒𝐝
❖ 𝐓𝟐𝟎 − 𝐓𝟏𝟐 = 𝟖𝐝
Therefore, 𝐓𝐧 − 𝐓𝐦 = ሺ𝐧 − 𝐦ሻ𝐝
Example 1 No-consecutive terms
3 differences
The difference between consecutive terms is 2. If
you were given that 7th term is 17 and 4th term is 11.
Determine the constant difference.
𝐓𝐧 − 𝐓𝐦 = ሺ𝐧 − 𝐦ሻ𝐝 − 𝐌𝐮𝐥𝐭𝐢𝐩𝐥𝐞 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐜𝐞
𝐓𝟕 − 𝐓𝟒 = 𝟑𝐝
𝟏𝟕 − 𝟏𝟏 = 𝟑𝐝
Therefore d = 2.
2|P age
