Sequences (Edexcel IGCSE Maths A: Higher): Exam Questions

Here are the first 5 terms of an arithmetic sequence.

3     9   15   21   27

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

Ben says that 150 is in the sequence.

Is Ben right?
You must explain your answer.

Here are the first four terms of an arithmetic sequence.

3   10   17   24

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

Is 150 a term of this sequence?
You must explain how you get your answer.

Here are the first five terms of an arithmetic sequence.

2   6   10   14   18

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

Is 86 a term in the sequence?

You must give a reason for your answer.

Here are the first four terms of an arithmetic sequence.

11   17   23   29

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

Is 121 a term of this arithmetic sequence?
You must explain your answer.

Here are the first four terms of an arithmetic sequence.

6   10   14   18

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

The $n$th term of a different arithmetic sequence is $3n+5$

Is 108 a term of this sequence?

Show how you get your answer.

Here are the first five terms of an arithmetic sequence.

4   9   14   19   24

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

Here are the first five terms of a different sequence.

2      2      0      -4      -10

An expression for the $n$th term of this sequence is $3n—n^2$

Write down, in terms of $n$, an expression for the $n$th term of a sequence whose first five terms are  

4      4      0      -8      -20

The  $n$th term of a number sequence is $n$² + 1

Write down the first three terms of the sequence.

A sequence has the terms

$\frac{1}{b^2},\frac{3}{b^2},\frac{5}{b^2}$...

Find out the number of terms that are less than 20 when $b=1.96$.

Here are the first four terms of a sequence of fractions.

$\frac{1}{1}\frac{2}{3}\frac{3}{5}\frac{4}{7}$

The numerators of the fractions form the sequence of whole numbers $1234...$

The denominators of the fractions form the sequence of odd numbers $1357...$

Write down an expression, in terms of $n$, for the $n\mathrm{th}$ term of this sequence of fractions.

Here are the first five terms of an arithmetic sequence.

Find the sum of the first 100 terms of this sequence.

Here are the first four terms of an arithmetic sequence.

$6101418$

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

Write down an expression, in terms of $n$, for the $(n+1)\mathrm{th}$ term of this sequence.

Here are the first five terms of a number sequence $S$.

$1016222834$

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

The $n\mathrm{th}$ term of a sequence $T$ is given by $n^2-3$

There are numbers that are terms in both the sequence $S$ and the sequence $T.$

Find one of these numbers.

A sunflower grows at a rate of 4 cm each day.

How many days does it take to grow from a height of 80 cm to more than 1.06 m?

If the sunflower grows at a faster rate, how would this affect your answer to part ($\mathbf{a}$)?

Here are the first five terms of a number sequence.

7        11        15        19        23

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

The $n$th term of a different number sequence is given by $80–2n$

Write down the first 3 terms of this sequence.

Yuen says there are no numbers that are in both of the sequences.
Yuen is correct.

Explain why.

The 3rd term of an arithmetic series is 25.
The sum of the first 10 terms is 350.
Find the 12th term.

The $n$th term of a sequence is $a{n}^2+bn$.

Write down an expression, in terms of $a$ and $b$, for the 3rd term.

The 3rd term of this sequence is 21 and the 6th term is 96.

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

Here are the first five terms of an arithmetic sequence.

2   5   8   11   14

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

Is 299 a term of this sequence?

You must give a reason for your answer.

Write down an expression, in terms of $n$, for the $(n+1)$th term of this sequence.

In all the following sequences, after the first two terms, the rule is to add the previous two terms to find the next term.

Write down the next two terms in this sequence.    

1    2    3    5    8    13      ...........      ...........

Write down the first two terms of this sequence.

.............       .............   3    11    14

(i) Find the value of d and the value of e.

      2    $d$     $e$  10

[3]

(ii) Find the value of x, the value of y and the value of z.

      -33    $x$    $y$    $z$    18

[5]

An arithmetic series has first term 1 and common difference 4.

Find the sum of all terms of the series from the 41st term to the 100th term inclusive.

The sum of the first $N$ terms of an arithmetic series, $S$, is 292

The 2nd term of $S$ is 8.5
The 5th term of $S$ is 13

Find the value of $N$.
Show clear algebraic working.

$N=$ ...................................................... 

Mario is going to save $50 in the year 2021

He is going to continue to save, up to and including the year 2070, by increasing the amount he saves each year by $\$k$

Mario will save a total of $33 125 from 2021 to 2070

Work out the value of $k$.

$k=$....................

The first term of an arithmetic series $S$ is –6
The sum of the first 30 terms of $S$ is 2865

Find the 9th term of $S$.

In an arithmetic series, the $6\mathrm{th}$ term is $39$
In the same arithmetic series, the $19\mathrm{th}$ term is $7.8$

Work out the sum of the first $25$ terms of the arithmetic series.

Work out the sum of the multiples of $3$ between $1$ and $1000$

Here are the first five terms of an arithmetic sequence.

$815222936$

Work out the sum of all the terms from the $50\mathrm{th}$ term to the $100\mathrm{th}$ term inclusive.

Theo starts with savings of £18

James starts with no savings.

Each week from now,

   Theo will save £4.50 and James will save £4

In how many weeks will Theo and James have savings in the ratio 15 : 8 ?

A sequence is defined using this term-to-term rule,

$u_{n+1}=k{u}_n+r$

where $k$ and $r$ are constants.

Given that $u_2=41$ , $u_3=206$ and $u_4=1031$, find the value of $k$ and the value of $r$.

$k$= ................

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

A sequence is defined by the rule $u_{n+1}=5u_n-15$

If $u_3=6$, calculate

(i) $u_5$

$u_5$=............................[3]

(ii)$u_2$

$u_2$=............................[3]

Here are the first 4 terms in an arithmetic sequence

3 7 11 15

The last term of the sequence is $x$
The sum of the terms of the sequence is 7260

Find the value of $x$
Show clear algebraic working.

An arithmetic series has first term $a$ and common difference $d$.

The sum of the first $2n$ terms of the series is four times the sum of the first $n$ terms of the series.

Find an expression for a in terms of $d$.
Show your working clearly.

The nth term of an arithmetic series is $u_n$ where $u_n>0$ for all $n$

The sum to $n$ terms of the series is $S_n$

Given that $u_4=6$ and that $S_{11}={\left(u_6\right)}^2+18$

find the value of $u_{20}$

Here are the first four terms of an arithmetic series.

$k$      $\frac{3k}{4}$     $\frac{k}{2}$     $\frac{k}{4}$

Given that the 15th term of the series is $(90+2k)$,
calculate the sum of the first 30 terms of the series.

$(2x+23),(8x+2)$ and $(20x–52)$ are three consecutive terms of an arithmetic sequence.

Prove that the common difference of the sequence is $12$

An arithmetic series has first term$a$ and common difference $d$, where $d$is a prime number.

The sum of the first n terms of the series is $S_n$and

$S_m=39$
$S_{2m}=320$

Find the value of $d$and the value of $m$ Show clear algebraic working.

$\begin{array}{rcl}d& =& ...................\\ m& =& ...................\end{array}$

The sum of the first 48 terms of an arithmetic series is 4 times the sum of the first 36 terms of the same series.

Find the sum of the first 30 terms of this series.

The 25th term of an arithmetic series is 44.5
The sum of the first 30 terms of this arithmetic series is 765

Find the 16th term of the arithmetic series.
Show your working clearly.

The $10\mathrm{th}$ term of an arithmetic series, $S$, is $66$
The sum of the first $20$ terms of $S$ is $1290$

Find the $5\mathrm{th}$ term of $S$.
Show your working clearly.

The 3rd term of an arithmetic series, $A$, is 19
The sum of the first 10 terms of $A$ is 290

Find the 10th term of $A$.

The sum of the first 80 terms of an arithmetic series, S, is 470

The 75th term of S is 14.5

The sum of the first X terms of S is 171

Work out the value of X
Show your working clearly