Arithmetic Sequences & Series (Edexcel A Level Maths: Pure): Exam Questions

In an arithmetic series

• the first term is 16

• the 21st term is 24

Find the common difference of the series.

Hence find the sum of the first 500 terms of the series.

A car has six forward gears.

The fastest speed of the car

• in 1^st gear is 28 km h^-1

• in 6^th gear is 115 km h^-1

Given that the fastest speed of the car in successive gears is modelled by an arithmetic sequence,

find the fastest speed of the car in 3rd gear.

The 4^th and 8^th terms of an arithmetic sequence are 20 and 64 respectively.

Find the first term, , and the common difference, .

The 12^th and 16^th terms of a different arithmetic sequence differ by 20.

Find the possible values of the common difference.

An arithmetic sequence is defined as follows:

• The first term is 3

• The 10^th term is 30

• The sum of the first  terms is 630

 Find the common difference.

Show that  satisfies the equation

Hence find the value of .

An arithmetic sequence is defined as follows:

• The third term is 2

• The twelfth term is 65

• The sum of the first  terms is 390

Show that 

Hence find the value of .

The sum of the first ten terms in an arithmetic series is 40. 

The sum of the first twenty terms in the same series is 280. 

Find the first term, , and the common difference, , of the series.

The first three terms in an arithmetic sequence are 

Find the value of .

The first three terms in an arithmetic sequence are 

Find the possible values of .

An arithmetic sequence is given by

where  is a constant.

Find a formula for the ^th term of the sequence, giving your answer in terms of and .

Show that the sum of the first  terms is given by

The sum of the first 12 terms is 39.

Find the value of .

Find the sum of all the odd numbers between 0 and 150:

An arithmetic sequence is given by

where is a constant.

Find an expression for the 100^th term of the sequence, giving your answer the form

where and are integers to be found.

The first two terms in an arithmetic sequence are  and 3. 

The fourth term is .

Find the value of .

An arithmetic sequence is defined as follows:

• The third term is

• The eleventh term is

• The sum of the first  terms is

Find the value of .

In an arithmetic series, the first term is and the common difference is .

Show that

James saves money over a number of weeks to buy a printer that costs

He saves in week 1, in week 2, in week 3 and so on, so that the weekly amounts he saves form an arithmetic sequence.

Given that James takes weeks to save exactly , show that

Solve the equation

Hence state the number of weeks James takes to save enough money to buy the printer, giving a brief reason for your answer.

The first three terms in an arithmetic sequence are 

Find the possible values of .

An arithmetic sequence has

• a first term of , where

• a common difference of

• a fifth term of 85

Find the ninth term in the sequence.

An arithmetic sequence is defined in terms of a constant, , as follows:

• The fifth term is

• The sum of the first eight terms is

Show that the first term of the sequence is

Find an expression for the common difference of the sequence in terms of only.

Given that the ninth term of the sequence is 14, find the value of .

Find the sum of the first 30 terms of the sequence.

The sum of the first twelve terms in an arithmetic series is 654.

The sum of the first twenty terms in the same arithmetic series is 530.

Find the 21^st term in the sequence.

Prove that the sum of the first  odd numbers is a square number, for any positive integer value of .

An arithmetic sequence is defined in terms of a constant, , as follows:

• The seventh term is

• The sum of the first nine terms is

Show that the common difference is and find an expression for the first term of the sequence, in terms of only.

Given that the 19^th term of the sequence is 57, find the sum of the first 25 terms.

The first four terms in an arithmetic sequence are 

Find the values of  and .

An arithmetic sequence is given by

where is a constant.

If the ^th term of the sequence is 36, show that

Hence show that the sum of the first  terms of the sequence is

Given that the sum of the first  terms of the sequence is 180, find the value of .

The first three terms in an arithmetic sequence are 

Given that these first three terms are all positive, find the value of the 40^th term in the sequence.

The sum of the first 24 terms in an arithmetic series is nine times the sum of the first two terms in the series.

Find the sum of the first 90 terms in the series.

An arithmetic sequence is given by

Find, in terms of , an exact expression for the sum of the first  terms of the sequence.

Hence find the smallest value of  for which the sum of the first  terms is greater than zero.

Express in the form , where and are constants, and .

Give the exact value of and give the value of in radians to 3 decimal places.

The first three terms of an arithmetic sequence are

Given that represents the sum of the first 9 terms of this sequence as varies,

(i) find the exact maximum value of

(ii) deduce the smallest positive value of at which this maximum value of occurs.

An arithmetic sequence has

• a first term of , where

• a common difference of

• a ninth term of 7

is the set of all the numbers that are in the sequence. 

 is the set of all rational numbers.

Find all the elements in the set .

The ^th term of an arithmetic series is 0.

The sum of the first  terms is also 0.

Find an expression for in terms of only, showing your working clearly.

For an arithmetic series

• the sum of the first 20 terms is 290

• the sum of the first 24 terms is -180

• the sum of the first  terms is

Find the greatest value that  can take, for any positive integer .

The th term in an arithmetic sequence is

Show that the sum of the first  terms of the sequence is given by

where  is a polynomial to be found, in terms of .