PAKISTAN INTERNATIONAL SCHOOL JEDDAH
ENGLISH SECTION
Mathematics (0580)
Grade: 10
Chapter: 9 Ex: 9.1 - 9.4
Sequences
Classwork
Academic Year Student Name Student ID Grade Level Date
2022 – 2023
2
1 Find the nth term of each sequence�
(a) 2, 6, 18, 54, 162, …
������������������������������������������������� [2]
(b) –1, –3, –5, –7, –9, …
................................................. [2]
(c) 24, 12, 6, 3, 1�5, f
................................................. [2]
1 2 3 4 5
( d)
3, , 5, 6, 7,
......
4
................................................. [1]
(e) –1, 0, 7, 26, 63, f
������������������������������������������������� [2]
3
(f) 0, 3, 8, 15, 24, ......
������������������������������������������������� [2]
2 32 25 18 11 4
These are the fi rst 5 terms of a sequence.
Find
(a) the 6th term,
................................................ [1]
(b) the nth term,
................................................ [2]
(c) which term is equal to –332.
................................................ [2]
3 The nth term of a sequence is 8 n 3.
-
(a) Write down the first two terms of this sequence.
....................... , ....................... [1]
(b) Show that the number 203 is not in this sequence.
[2]
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4
4 … , 20, 50, …
The second term of this sequence is 20 and the third term is 50.
The rule for finding the next term in this sequence is subtract y then multiply by 5.
Find the value of y and work out the first term of this sequence.
y = ................................................
First term = ................................................ [4]
5 The nth term of a sequence is an 2 + bn - 4 .
The first term is - 3 and the second term is 2.
Find the value of a and the value of b.
a = ................................................
b = ................................................ [5]
5
6 (a) Complete the table for the 5th term and the nth term of each sequence.
[11]
(b) 0, 1, 1, 2, 3, 5, 8, 13, 21, …
This sequence is a Fibonacci sequence.
After the first two terms, the rule to find the next term is “add the two previous terms”.
For example, 5 + 8 = 13.
Use this rule to complete each of the following Fibonacci sequences.
2 4 ............ ............ ............
1 ............ ............ ............ 11
............ -
1 ............ ............ 1
[3]
1 3, 4 7, 11
(c) , , , …
3 4 7 11 18
p
(i) One term of this sequence is q .
Find, in terms of p and q, the next term in this sequence.
.................................................... [1]
(ii) Find the 6th term of this sequence.
.................................................... [1]
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6
Diagram 1 Diagram 2 Diagram 3
The first three diagrams in a sequence are shown above.
Diagram 1 shows an equilateral triangle with sides of length 1 unit.
1
In Diagram 2, there are 4 triangles with sides of length 2 unit.
1
In Diagram 3, there are 16 triangles with sides of length 4 unit.
(a) Complete this table for Diagrams 4, 5, 6 and n.
Diagram 1 Diagram 2 Diagram 3 Diagram 4 Diagram 5 Diagram 6 Diagram n
1 1
Length of side 1 2 4
Length of side
20 2 –1 2 –2
as a power of 2
[6]
(b) (i) Complete this table for the number of the smallest triangles in Diagrams 4, 5 and 6.
Diagram 1 Diagram 2 Diagram 3 Diagram 4 Diagram 5 Diagram 6
Number of smallest
1 4 16
triangles
Number of smallest
20 22 24
triangles as a power of 2
[2]
(ii) Find the number of the smallest triangles in Diagram n, giving your answer as a power of 2.
................................................ [1]
(c) Calculate the number of the smallest triangles in the diagram where the smallest triangles have sides of
1 unit.
length 128
................................................ [2]
7
Diagram 1 Diagram 2 Diagram 3
The diagrams show a sequence of dots and circles.
Each diagram has one dot at the centre and 8 dots on each circle.
The radius of the first circle is 1 unit.
The radius of each new circle is 1 unit greater than the radius of the previous circle.
(a) Complete the table for diagrams 4 and 5.
Diagram 1 2 3 4 5
Number of dots 9 17 25
Area of the largest circle π 4π 9π
Total length of the circumferences of the circles 2π 6π 12π
[4]
(b) (i) Write down, in terms of n, the number of dots in diagram n.
................................................ [2]
(ii) Find n, when the number of dots in diagram n is 1097.
n =................................................ [2]
(c) Write down, in terms of n and π, the area of the largest circle in
(i) diagram n,
................................................ [1]
(ii) diagram 3n.
................................................ [1]
(d) Find, in terms of n and π, the total length of the circumferences of the circles in diagram n.
................................................ [2]
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8
9 (a) The nth term of a sequence is n(n+1).
(i) Write the two missing terms in the spaces. 2, 6, , 20, [2]
(ii) Write down an expression in terms of n for the (n + 1)th term.
................................................ [1]
(iii) The difference between the nth term and the (n + 1)th term is pn + q.
Find the values of p and q.
p = ................................................
q = ................................................ [2]
(iv) Find the positions of the two consecutive terms which have a difference of 140.
........... and ........... [2]
(b) A sequence u1, u2, u3, u4, …………. is given by the following rules.
u1 = 2, u2 = 3 and un = 2u n − 2 + u n −1 for n [ 3.
For example, the third term is u3 and u3 = 2u1 + u2 = 2 × 2 + 3 = 7.
So, the sequence is 2, 3, 7, u4, u5, …..
(i) Show that u4 = 13.
................................................................................................ ................................................ [1]
(ii) Find the value of u5 .
u5 = ................................................ [1]
(iii) Two consecutive terms of the sequence are 3413 and 6827 .
Find the term before and the term after these two given terms.
................................................ , 3413, 6827, ................................................ [2]
PAKISTAN INTERNATIONAL SCHOOL JEDDAH
ENGLISH SECTION
Mathematics (0580)
Grade: 10
Chapter: 9 Ex: 9.1 - 9.4
Sequences
Homework
Academic Year Student Name Student ID Grade Level Date
2022 – 2023
2
1 Find the nth term of each sequence�
(a) 15 7 −1 -9
.................................................[2]
(b) 3, 6, 12, 24, …
................................................. [2]
(c) 1 , 1 , 1 , 1 , 1 , ...
2 4 6 8 10
................................................. [1]
(d) 64, 16, 4, 1, …
................................................. [2]
(e) 3, 17, 55, 129, 251, …
................................................. [2]
3
2 A sequence is given by u1 = 1 , u2 = 3, u3 = 5, u4 = 7,…
(a) Find a formula for un , the nth term.
u n = ................................................... [2]
(b) Find u29 .
u29 = ................................................... [1]
3 19, 15, 11, 7, .... ....
(a) Write down the next two terms of the sequence.
...................... , .................. [2]
(b) Find the nth term of this sequence.
............................................... [2]
(c) Find the value of n when the nth term is -65.
n = ............................................... [2]
..............................................
4 The nth term of a sequence is n 2 + 3n .
Find the first three terms of this sequence.
............., ............., ............. [2]
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4
5 (a) These are the first five terms of a sequence.
27 26 23 18 11
Find the next two terms in the sequence.
....................... , ....................... [2]
(b) The table shows information about two different sequences.
First five terms of sequence nth term
Sequence A 3 10 17 24 31
Sequence B 2 11 26 47 74
Complete the table.
[4]
6 The table shows the first five terms of sequences A, B and C.
1st term 2nd term 3rd term 4th term 5th term nth term
Sequence A 8 3 -2 -7 -12
Sequence B 2 3 4 5 6
2 3 4 5
1 1 2 4 8
Sequence C
2
Complete the table to show the nth term of each sequence.
[5]
5
Diagram 1 Diagram 2 Diagram 3 Diagram 4
These are the first four diagrams of a sequence.
The diagrams are made from white dots and black dots.
(a) Complete the table for Diagram 5 and Diagram 6.
Diagram 1 2 3 4 5 6
Number of white dots 1 4 9 16
Number of black dots 0 1 3 6
Total number of dots 1 5 12 22
[2]
(b) Write an expression, in terms of n, for the number of white dots in Diagram n.
................................................. [1]
(c) The expression for the total number of dots in Diagram n is 1 (3n 2 - n) .
2
(i) Find the total number of dots in Diagram 8.
................................................. [1]
(ii) Find an expression for the number of black dots in Diagram n.
Give your answer in its simplest form.
................................................. [2]
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6
8
Layer 1
Layer 2
Layer 3
The diagrams show layers of white and grey cubes.
Khadega places these layers on top of each other to make a tower.
(a) Complete the table for towers with 5 and 6 layers.
Number of layers 1 2 3 4 5 6
Total number of white cubes 0 1 6 15
Total number of grey cubes 1 5 9 13
Total number of cubes 1 6 15 28
[4]
(b) (i) Find, in terms of n, the total number of grey cubes in a tower with n layers.
................................................ [2]
(ii) Find the total number of grey cubes in a tower with 60 layers.
................................................ [1]
(iii) Khadega has plenty of white cubes but only 200 grey cubes.
How many layers are there in the highest tower that she can build?
................................................ [2]
7
(c) The expression for the total number of white cubes in a tower with n layers is pn2 + qn + 3.
Find the value of p and the value of q.
Show all your working.
p = ................................................
q = ................................................ [5]
(d) Find an expression, in terms of n, for the total number of cubes in a tower with n layers.
Give your answer in its simplest form.
................................................ [2]
[Turn over
