OPM1501
Assignment 3
Unique No:147506
DUE 7 July 2025
,Analysis of Number Sets and Flow Diagrams
1.1. Pattern Recognition in Number Sets
Identifying patterns in number sequences is a cornerstone of mathematical reasoning, vital
for comprehending sequences, series, and the very nature of mathematical functions. A true
pattern implies a consistent, definable rule that dictates the relationship between elements
within a set (Stewart, 2018). Let’s examine each set to determine if a discernible pattern
exists:
Number Set Pattern or Description
Not
1; 3; 5; 7; 9; ... A pattern This is a classic arithmetic progression. Each subsequent term is derived
by adding a constant difference of 2 to the preceding term. The general
formula for such a sequence is a n = a1 +(n−1)d, where a1 = 1 (the first term)
and d = 2 (the common difference). This consistent additive relationship
clearly defines a pattern.
2; 3; 4; 4; 6; 5; Not a There’s no consistent mathematical rule governing this sequence. While
8 ... pattern some numbers increment, the repetition of ’4’ and the varying differences
between terms (e.g., 3−2 = +1, 4−4 = 0, 6 − 4 = +2) contradict the notion of
a uniform pattern. A true pattern demands predictability, which is absent
here.
9; 18; 729; Not a Initially, one might observe 9 × 2 = 18, suggesting a geometric progression.
6569; ... pattern However, the subsequent leaps from 18 to 729 and then to 6569 do not
adhere to this or any other simple arithmetic or geometric rule. The erratic
jumps demonstrate a lack of consistent progression, precluding it from
being classified as a pattern.
7; 8; 10; 12; 14; A pattern This sequence exhibits a piecewise pattern. While the jump from 7 to 8 is
... +1, from the third term onwards, it functions as an arithmetic progression
with a common difference of 2 (8 + 2 = 10, 10 + 2 = 12, 12 + 2 = 14). This
structure, though not uniformly arithmetic from the very first term, is
clearly definable and predictable after the initial two terms.
1
, 14; 28; 34; 41; Not a The differences between consecutive terms are highly inconsistent: 28 − 14
48; ... pattern = +14, 34 − 28 = +6, 41 − 34 = +7, 48 − 41 = +7. The absence of a constant
difference or ratio, or any other discernible mathematical relationship
across all terms, means this sequence lacks a definable pattern.
—
Navigating Flow Diagram 1
Flow diagrams visually depict a series of operations or decisions. To complete this diagram,
we infer the operations between steps, building a logical sequence.
• (a) - 6
• (b) - 10
• (c) - 15
• (d) - 19
• (e) - 24
• (f) - 28
Justification: The sequence reveals an alternating additive pattern: The pattern starts by
adding 4, then 4 again, then 5, then 4, then 5, and so on. Assuming an initial value that
allows for this consistent progression (e.g., if the input to ’a’ was 2), the sequence unfolds
as: 2+46(a) 6+410(b)
10+515(c)
15+419(d)
19+524(e)
24+428(f)
—
2
Assignment 3
Unique No:147506
DUE 7 July 2025
,Analysis of Number Sets and Flow Diagrams
1.1. Pattern Recognition in Number Sets
Identifying patterns in number sequences is a cornerstone of mathematical reasoning, vital
for comprehending sequences, series, and the very nature of mathematical functions. A true
pattern implies a consistent, definable rule that dictates the relationship between elements
within a set (Stewart, 2018). Let’s examine each set to determine if a discernible pattern
exists:
Number Set Pattern or Description
Not
1; 3; 5; 7; 9; ... A pattern This is a classic arithmetic progression. Each subsequent term is derived
by adding a constant difference of 2 to the preceding term. The general
formula for such a sequence is a n = a1 +(n−1)d, where a1 = 1 (the first term)
and d = 2 (the common difference). This consistent additive relationship
clearly defines a pattern.
2; 3; 4; 4; 6; 5; Not a There’s no consistent mathematical rule governing this sequence. While
8 ... pattern some numbers increment, the repetition of ’4’ and the varying differences
between terms (e.g., 3−2 = +1, 4−4 = 0, 6 − 4 = +2) contradict the notion of
a uniform pattern. A true pattern demands predictability, which is absent
here.
9; 18; 729; Not a Initially, one might observe 9 × 2 = 18, suggesting a geometric progression.
6569; ... pattern However, the subsequent leaps from 18 to 729 and then to 6569 do not
adhere to this or any other simple arithmetic or geometric rule. The erratic
jumps demonstrate a lack of consistent progression, precluding it from
being classified as a pattern.
7; 8; 10; 12; 14; A pattern This sequence exhibits a piecewise pattern. While the jump from 7 to 8 is
... +1, from the third term onwards, it functions as an arithmetic progression
with a common difference of 2 (8 + 2 = 10, 10 + 2 = 12, 12 + 2 = 14). This
structure, though not uniformly arithmetic from the very first term, is
clearly definable and predictable after the initial two terms.
1
, 14; 28; 34; 41; Not a The differences between consecutive terms are highly inconsistent: 28 − 14
48; ... pattern = +14, 34 − 28 = +6, 41 − 34 = +7, 48 − 41 = +7. The absence of a constant
difference or ratio, or any other discernible mathematical relationship
across all terms, means this sequence lacks a definable pattern.
—
Navigating Flow Diagram 1
Flow diagrams visually depict a series of operations or decisions. To complete this diagram,
we infer the operations between steps, building a logical sequence.
• (a) - 6
• (b) - 10
• (c) - 15
• (d) - 19
• (e) - 24
• (f) - 28
Justification: The sequence reveals an alternating additive pattern: The pattern starts by
adding 4, then 4 again, then 5, then 4, then 5, and so on. Assuming an initial value that
allows for this consistent progression (e.g., if the input to ’a’ was 2), the sequence unfolds
as: 2+46(a) 6+410(b)
10+515(c)
15+419(d)
19+524(e)
24+428(f)
—
2
