Sequences (Cambridge (CIE) O Level Maths): Exam Questions

In a sequence

$T_1=17T_2=12T_3=7T_4=2.$

Find

$T_5$

Find $T_n$.

The nth term of a sequence is $60-8n$.

Find the largest number in this sequence.

Here are the first five terms of a different sequence.

12          19          26          33          40

Find an expression for the $n$th term of this sequence.

[2]

Here is a sequence of numbers.

7,   5,   3,   1,   – 1, …

Find an expression for the $n$th term of this sequence.

These are the first four terms of a sequence.

i) Write down the next term.  

[1]

ii) Find an expression, in terms of n, for the nth term.  

[2]

Write down the next two terms of the sequence.

Find the $n$th term of this sequence.  

[2]

Find the value of $n$ when the $n$th term is -65.  

$n$ = .............................................. 

These are the first five terms in a sequence.  

$811141720$

Find an expression for the $n$th term.

These are the first five terms of a sequence.

$-4281420$

  Find an expression for the $n$th term of this sequence.

Marco is making patterns with grey and white circular mats.

The patterns form a sequence. Marco makes a table to show some information about the patterns.

Complete the table for Pattern 5.

Find an expression, in terms of $n$, for the number of grey mats in Pattern $n$.

Marco makes a pattern with 24 grey mats. Find the total number of mats in this pattern.

Find an expression for the $n$th term of the sequence below.

$11,7,3,-1,...$

$\frac{1}{3},\frac{3}{4},\frac{4}{7},\frac{7}{11},\frac{11}{18},...$

i) One term of this sequence is $\frac{p}{q}$.
Find, in terms of $p$ and $q$, the next term in this sequence.

[1]

ii) Find the 6th term of this sequence.

[1]

These are the first five terms of a sequence.

Find the next term.

Find the next term and the $n$th term of this sequence.

$\frac{3}{5},\frac{4}{7},\frac{5}{9},\frac{6}{11},\frac{7}{13},...$

Next term = .................................................  
$n$th term = ................................................. 

The $n$th term of a sequence is given by $a{n}^2+bn$ where $a$ and $b$ are integers.

The 2nd term of the sequence is —2
The 4th term of the sequence is 12

Find the 6th term of the sequence.

Here are the first five terms of a different quadratic sequence.

0   2   6   12   20

Find an expression, in terms of $n$, for the $n$th term of this sequence.

Find the $n$th term of each sequence.

4,   8,   12,   16,   20,   .........

11,   20,   35,   56,   83,   ..........

Here are the first six terms of a Fibonacci sequence.

            1   1   2   3         5    8

The rule to continue a Fibonacci sequence is,

         the next term in the sequence is the sum of the two previous terms.

Find the 9th term of this sequence.

The first three terms of a different Fibonacci sequence are

$aba+b$

Show that the $6$th term of this sequence is $3a+5b$

Given that the 3rd term is 7 and the 6th term is 29,

find the value of $a$ and the value of $b$.

Grey squares and white squares are used to make patterns in a sequence. The first three patterns in the sequence are shown. Pattern 4 is incomplete.

Shade squares in Pattern 4 to continue the sequence.

Complete the table for the patterns in the sequence.

i) Write an expression, in terms of $n$, for the number of grey squares in Pattern $n$.

[2]

ii) Write an expression, in terms of $n$, for the number of white squares in Pattern $n$.

[2]

Pattern 10 and Pattern 11 in the sequence are made from grey squares and white squares.

Find the difference between the total number of squares needed to make Pattern 10 and the total number of squares needed to make Pattern 11.

Pattern $k$ in the sequence needs 61 grey squares.
Find the number of white squares needed for Pattern $k$.

Empty circles and filled-in circles are used to make the patterns in a sequence.
The first three patterns in the sequence are shown below.
Pattern 4 is incomplete.

Fill in circles in Pattern 4 to complete the sequence.

Complete the table below for the numbers of empty and filled in circles in the sequence.

Write an expression in terms of $n$ for the number of empty circles in Pattern $n$.

Write an expression in terms of $n$ for the number of filled in circles in Pattern $n$.

Find the total number of circles in Pattern 12.

Pattern $k$ in the sequence needs 122 filled in circles.

Find the number of empty circles needed for Pattern $k$.

Complete the table for the three sequences.

One term in Sequence C is $\frac{p}{q}$.
Write down the next term in Sequence $C$ in terms of $p$and $q$.

The sequence of diagrams above is made up of small lines and dots.

Complete the table.

For Diagram $n$ find an expression, in terms of $n$, for the number of small lines. 

Diagram $r$ has 10 300 small lines.  

Find the value of $r$.  

$r$ = .............................................. 

The number of dots in Diagram $n$ is $a{n}^2+bn+1$.  

Find the value of $a$ and the value of $b$.  

$a$ = .............................................. 
$b$ = .............................................. 

The table shows the first five terms of sequence A and sequence B.

Complete the table for the 6th term of each sequence.

i) Find the $n$th term of sequence A.  

[2]

ii) Find the $n$th term of sequence B.  

[2]

The first four terms $u_{\mathbf{1}},u_{\mathbf{2}},u_{\mathbf{3}}$, and $u_{\mathbf{4}}$in a sequence of numbers are given by

$$\begin{gathered} u_{\mathbf{1}}=\mathbf{1}\times 2+3^2=11 \\ {u}_{\mathbf{2}}=\mathbf{2}\times 3+4^2=22 \\ {u}_{\mathbf{3}}=\mathbf{3}\times 4+5^2=37 \\ {u}_{\mathbf{4}}=\mathbf{4}\times 5+6^2=56. \end{gathered}$$

 Evaluate $u_{\mathbf{5}}$.

The $n$th term of the sequence is $u_n$.

Write down an expression for $u_n$ in terms of $n$.

 Given that $u_n=A{n}^2+Bn+C$, find the values of $A,B$ and $C$.

$A=$................

$B=$.................

$C=$.................