Special sequences

Write down the next number in the sequence

1 4 7 10

Write down the next number in the sequence

2 4 8 16

Write down the next number in the sequence

20 14 8 2

Work out 3 × (– 6)

Write the missing term in the geometric progression.

A Fibonacci-type sequence begins

5 – 9

The sequence is continued by adding the previous two terms.

Work out the next two terms.

Write the missing term in the geometric progression.

A Fibonacci-type sequence begins

5 – 9

The sequence is continued by adding the previous two terms.

Work out the next two terms.

A linear sequence starts

4 7 10 13

Write down the next number in this sequence.

A different linear sequence starts

19 14 9 4

Write down the next number in this sequence.

Here is another sequence.

3 6 12 24

Write down the term-to-term rule for this sequence.

A linear sequence has

1st term = 10

1st term + 2nd term = 39

Work out the 5th term.

Work out the next term.

The nth term of a geometric progression is rⁿ where r 0

Work out the third term.

A computer game has five levels. Each level has a maximum number of points. These maximum numbers form an arithmetic progression. The table shows the numbers for the first three levels.

Your score is the total of the points you achieve in each of the five levels. Isaac’s best score is 1250 points less than the highest possible score.

Work out his best score.

Four consecutive triangular numbers are 6 10 15 21 Write down the next triangular number.

Match the name to the correct sequence. One has been done for you.

Name Sequence

The 47th triangular number is 1128 The 48th triangular number is 1176 Work out the 49th triangular number.

The x-values in the table make a linear sequence. The y-values in the table make a different linear sequence.

Complete the table.

Draw a straight line passing through the points (0, 3), (2, 7) and (4, 11)

Use the graph to work out the value of y when x = 3

Here is the rule for a sequence. After the first two terms, each term is the sum of the previous two terms The 1st term is 33 The 2nd term is x The 4th term is 73 Work out the value of x.

x =

An expression for the nth term of a different sequence is n – n² Ruth says, ‘‘All the terms will be negative because n² is always greater than n.’’ Is she correct?

Give a reason for your answer.

Here is the rule for a sequence.

After the first two terms, each term is the sum of the previous two terms

The 1st term is 33 The 2nd term is x The 4th term is 73

Work out the value of x.

An expression for the nth term of a different sequence is n – n² Ruth says, ‘‘All the terms will be negative because n² is always greater than n.’’

Is she correct?

Give a reason for your answer.

Circle the triangular number.

9 12 15 18

A is an arithmetic progression. Here are the first four terms. 13 16 19 22

G is a geometric progression. Here are the first four terms. 2 4 8 16

Work out the value of n.

n =

Here is a rule for a sequence. After the first two terms, each term is the sum of the previous two terms. The first five terms are p 23 q 57 r Work out the values of p, q and r.

The first three terms of a geometric progression are Circle the fourth term.

All the terms of a geometric progression are positive. The second and fourth terms are shown. ………. 4 ………. 16 Work out the first and third terms.

The first two terms of an arithmetic progression are shown. p 5 p ….. The sum of the first three terms is 90 Work out the value of p.

All the terms of a geometric progression are positive. The second and fourth terms are shown. ………. 4 ………. 16 Work out the first and third terms.

The first two terms of an arithmetic progression are shown. p 5 p ….. The sum of the first three terms is 90 Work out the value of p.

A geometric progression starts 4 16 Work out the next term.

A Fibonacci-type sequence starts 3 – 8 The sequence is continued by adding the previous two terms. Work out the next two terms.

A geometric progression starts 4 16 Work out the next term.

A Fibonacci-type sequence starts 3 – 8 The sequence is continued by adding the previous two terms. Work out the next two terms.

The first four triangular numbers are 1, 3, 6, 10 Circle the next triangular number.

14 15 16 19

Which of these is a geometric progression? Circle your answer.

1 3 5 7 9 1 3 6 10 15

1 4 9 16 25 1 3 9 27 81

Match each sequence to its description. One has been done for you.

Match each sequence to its description. One has been done for you.

Work out the next term of this quadratic sequence.

5 8 14 23 ……

Work out the next term of this quadratic sequence.

5 8 14 23 ……

x – 1 28 y = p × q where p and q are numbers. y = 10 when x = 1 y = 0.3125 when x = 6 Work out the value of y when x = 3

Which of these is a geometric progression? Circle your answer.

2, 4, 6, 8, 10
2, 3, 5, 8, 12

2, 6, 18, 54, 162
2, 6, 10, 14, 18

Here are some numbers. 10 13 15 20 27 39

10 15 20 is an arithmetic progression. Use three of the numbers to make a different arithmetic progression. Describe the rule.