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

Find the $n$th term of the sequence below. $\frac{1}{2},\frac{1}{4},\frac{1}{6},\frac{1}{8},\frac{1}{10},...$

The $n$th term of a sequence is $4n^2+n+3.$

i) Find the 2nd term.  

[1]

ii) Find the value of $n$ when the $n$th term is 498.  

$n=$.................................................. [3]

Here is a sequence.

$a,13,9,3,-5,-15,b,...$

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

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

Find the $n$th term of each sequence.

4        2        0        -2        -4        ...

1        7        17        31        49        ...

Complete the table for the 5th term and the nth term of each sequence.

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.

$$\begin{gathered} 24........................ \\ 1........................11 \\ ........-1................1 \end{gathered}$$

Find the $n$th term of the sequence below.

$1,5,25,125,625,...$

Find the $n$th term of each sequence.

i) $-1,-3,-5,-7,-9,...$

[2]

ii) $2,9,28,65,126,...$  

[2]

Find the $n$th term of the sequence below.

$3,6,12,24,...$

These are the first four diagrams of a sequence. The diagrams are made from white dots and black dots.

Complete the table for Diagram 5 and Diagram 6.

Write an expression, in terms of $n$, for the number of white dots in Diagram $n.$

The expression for the total number of dots in Diagram $n$ is  $\frac{1}{2}\left(3n^2-n\right)$.

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]

$T$is the total number of dots used to make all of the first  $n$ diagrams.

$T=a{n}^3+b{n}^2$ 

Find the value of $a$ and the value of $b$. You must show all your working.

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

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

The table shows the first four terms in sequences A, B, and C.

Complete the table.

The table shows the first five terms of sequences A, B and C.

Complete the table.

Find an expression for the $n$th term of

i) sequence A,  

[2]

ii) sequence B.  

[1]

Find the value of $n$ when the $n$th term of sequence A is 576.  

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

i) Find an expression for the $n$th term of sequence C.
Give your answer in its simplest form.  

[3]

ii) Find the value of the 30th term of sequence C.  

[2]