The nth term

An arithmetic series has 30 terms.

The first term is a The common difference is d

The 20th term is 123 The sum of the 30 terms is 2880

Work out the value of a and the value of d Show clear algebraic working.

Here are the first four terms of an arithmetic sequence.

1 4 7 10

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

The nth term of a different arithmetic sequence is 5n + 17

Find the 12th term of this sequence.

Here are the first four terms of an arithmetic sequence.

1 4 7 10

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

The nth term of a different arithmetic sequence is 5n + 17

Find the 12th term of this sequence.

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.

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.

An arithmetic sequence has first term 8 and common difference 11 The sequence has k terms, where k 21

The sum of the last 20 terms of the sequence is 10 170

Find the value of k Show clear algebraic working.

Here are the first five terms of an arithmetic sequence.

1 5 9 13 17

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

The nth term of another arithmetic sequence is 3n + 5

Find an expression, in terms of m, for the (2m)th term of this sequence.

Here are the first five terms of an arithmetic sequence.

1 5 9 13 17

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

The nth term of another arithmetic sequence is 3n + 5

Find an expression, in terms of m, for the (2m)th term of this sequence.

In a warehouse there are two types of shelves, type R and type S.

These two types of shelves are arranged into shelving units that form a sequence of patterns.

Here are the first three terms in the sequence.

The width of each type R shelf is 2.4 m and the width of each type S shelf is 3.5 m

Work out the total width of a shelving unit that has 6 type R shelves.

A shelving unit has n type R shelves. The total width of this shelving unit is W metres.

Find an expression for W in terms of n Give your answer in its simplest form.

The sum of the first 10 terms of an arithmetic series is 4 times the sum of the first 5 terms of the same series.

The 8th term of this series is 45

Find the first term of this series. Show clear algebraic working.

In an arithmetic series, the 6th term is 39 In the same arithmetic series, the 19th term is 7.8

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

Here is a sequence of patterns made from square tiles.

Pattern number 1
Pattern number 2
Pattern number 3

In the space below, draw Pattern number 4

Complete the table.

Work out the number of tiles in Pattern number 30

Liz says that in Pattern number n, the number of tiles is 2n.

Is Liz correct? You must give a reason for your answer.

Here is a sequence of patterns made from circles.

number 1
number 2
number 3
number 4

In the space below, draw Pattern number 5

Complete the table.

Work out the number of circles in Pattern number 8

C is the number of circles in Pattern number P

Write down a formula for C in terms of P

A different sequence of patterns is made from triangles. The rule to find the number of triangles in each pattern is

multiply the Pattern number by 5 and subtract 4

Is there a pattern in this sequence that is made from exactly 136 triangles? You must give a reason for your answer.

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.

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.

Here are the first four terms of an arithmetic sequence.

6 10 14 18

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

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

Here is a sequence of patterns made from dots.

Pattern Pattern Pattern Pattern number 1 number 2 number 3 number 4

Draw Pattern number 4 in the space above.

Complete the table.

Work out the number of dots in Pattern number 13

Find an expression, in terms of n, for the number of dots in Pattern number n.

There are fewer than 90 dots in Pattern number k.

What is the largest possible value of k ?