Sequences (Cambridge International IGCSE Mathematics): Exam Questions

Here is a sequence of numbers.

7, 5, 3, 1, – 1, …

Find the next term in this sequence.

Write the next term in each of these sequences.

i) 1 1 2 3 5 8

ii) 2 4 8 16 32 64

This expression can be used to generate a sequence of numbers.

$n^{2}-n+11$

i) Work out the first three terms of this sequence.

ii) Show that this expression does not only generate prime numbers.

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.

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 $b$.

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

$912172433$

Write down the next term in the sequence.

Find the $n^{\mathrm{th}}$ term of the sequence.

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.

$24........................\,\,1........................11\,\,........-1................1$

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

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

Find the $n$th term of each sequence.

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

ii) $2,9,28,65,126,...$

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.

Extract:

| Diagram | 1 | 2 | 3 | 4 | 5 | 6 | | Number of white dots | 1 | 4 | 9 | 16 | | |

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

Extract:

| 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 | | |

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 $1 \frac{1}{2} ( 3 n^{2} - n )$.

i) Find the total number of dots in Diagram 8.

ii) Find an expression for the number of black dots in Diagram $n.$ Give your answer in its simplest form.

Extract:

| 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 | | |

The expression for the total number of dots in Diagram n is 1/2 (3n^2 − n).

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

$T=an^{3}+bn^{2}$

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.

Extract:

| Sequence | 1st term | 2nd term | 3rd term | 4th term | 5th term | 6th term | | A | 0 | 1 | 4 | 9 | 16 | | | B | 4 | 5 | 6 | 7 | 8 | |

Find an expression for the $n$th term of

i) sequence A,

ii) sequence B.

Extract:

Find an expression for the nth term of i) sequence A.

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

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

Extract:

| Sequence | 1st term | 2nd term | 3rd term | 4th term | 5th term | 6th term | | C | -4 | -4 | -2 | 2 | 8 | |

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

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