Number
Pattern
Questions on number pattern can be
set in Paper 1 and Paper 2.
Number Pattern questions in Paper 2
are usually long and the "O" level examiners will always give a
numerical example on the number pattern. Students are advised to
study the example carefully and identify the pattern(s) based on
the given numerical example. Next, questions will be asked based on
the identified patterns.
Number Pattern questions in Paper 1
will be
(1) Write
down the next two terms in the sequence
(2) Given
the nth term formula, write down the first 4
terms
(3) Given the nth
term formula, find the nth term eg 7th term.
(4)* Given the
numerical sequence, find the nth term formula.
These are the common number
patterns (nth term formula) that are set in the "O" level E.Maths
exam.
Pattern
1
5, 7, 9, 11, 13,
.....
Since the pattern is +2, + 2,
the nth term formula will be 2n + a
n = 1, 2(1) + 3 =
5
n = 2, 2(2) + 3 =
7
So, the nth term forrmula is
2n + 3
Pattern 2
3, 5, 9, 17, 33,
.....
Since the pattern is +2, + 4, + 8,
......,
ie
+2^1, +2^2, +2^3
so the nth term formula will be 2^n
+ a
n = 1, 2^1 + 1 =
3
n = 2, 2^2 + 1 =
5
n = 3, 2^3 + 1 =
9
So, the nth
term formula will be 2^n + 1
Pattern 3
4, 7, 12, 19,
.....
Since the pattern is +3, +5,
+7, the nth term formula will be
n^2 + a
n = 1, 1^2 + 3 =
4
n = 2, 2^2 + 3 =
7
n = 3, 3^2 + 3 =
12,
So, the nth term formula is n^2
+3.
Pattern 4
1, 3, 6, 10,
......
Since the pattern is +2, +3, +4,
...., the nth term formula will be
1/2[(n+a)(n+b)]
n = 1, (1/2)[(n+a)(n+b)] =
1/2[(1+0)(1+1)] = 1
n = 2, (1/2)[(n+a)(n+b)] =
1/2[(2+0)(2+1)] = 3
n = 3, (1/2)[(n+a)(n+b)] =
1/2[(3+0)(3+1)] = 6
n = 4, (1/2)[(n+a)(n+b)] =
1/2[(4+0)(4+1)] = 10
So, the nth term pattern will be
(1/2)[(n)(n+1)]
PS : Students who have calculators with
equation function eg Casio FX 95 MS or Sharp EL
509WS can make use its ability to solve
for the 3 unknowns using the simultaneous equations mode for
Patterns 1, 3 and 4 except pattern 2 to find the nth term
formula
Paper 1 Exam Questions on Number
Patterns
(1) Write
down an expression, in terms of n, for the nth
term
in this sequence 4, 9, 16, 25,
..... (Pattern
?)
(2) Write
down an expression, in terms of n, for the nth
term
in this sequence 2, 7, 12, 17, 22,
..... (Pattern ?)
(3) Write
down an expression, in terms of n, for the nth
term
in this sequence 4, 7, 10, 13,
..... (Pattern
?)
(4) Write
down an expression, in terms of n, for the nth
term
in this sequence 4, 7, 12, 19,
28, ..... (Pattern ?)
(5) Write
down an expression, in terms of n, for the nth
term
in this sequence 0, 3, 8,
15,.....
(Pattern ?)
(6) Write
down an expression, in terms of n, for the nth
term
in this sequence 5, 9, 13, 17,
21,..... (Pattern ?)
(7) Write
down an expression, in terms of n, for the nth
term
in this sequence 1, 4, 7, 10,
13, .... (Pattern
?)
(8) Write
down an expression, in terms of n, for the nth
term
in this sequence 1, 3, 6, 10, 15, 21,..... (Pattern
?)
(9) Write
down an expression, in terms of n, for the nth
term
in this sequence 3, 6, 10, 15,
21,..... (Pattern
?)
(10) Write down an
expression, in terms of n, for the nth term
in this sequence 1, 7, 17, 31,
.....
(Pattern ?)
(11) Write down
an expression, in terms of n, for the nth
term in this sequence 0, 3, 8, 15, 24,
..... (Pattern
?)
Students are advised to practise on
these questions to familarize themselves with the different
patterns asked in the "O" level Exam on E.Maths.
Thank you for your kind
attention.
Regards,
ahm97sic
