Sequences

Here are the first three patterns in a sequence.

Draw Pattern 4 on the grid.

How many squares in Pattern 6 would have a cross (X) in them?

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.

Here are the first three terms of a linear sequence.

5 11 17

Write down the next term.

Describe the term-to-term rule.

Here are the first three Patterns in a sequence made up of small squares.

On the grid, draw Pattern 4

The expression for the number of small squares in Pattern n is n² + 4

Work out the least value of n for which the number of small squares is greater than 500

n =

Here are the first three Patterns in a sequence made up of small squares.

On the grid, draw Pattern 4

The expression for the number of small squares in Pattern n is n² + 4

Work out the least value of n for which the number of small squares is greater than 500

n =

Here is the term-to-term rule for a sequence.

The first three terms of the sequence are a + 1 2 a + 5 4 a + 13

Show that the sum of the first four terms is a multiple of 3

Here is the term-to-term rule for a sequence.

The first three terms of the sequence are a + 1 2 a + 5 4 a + 13

Show that the sum of the first four terms is a multiple of 3

The term-to-term rule for a sequence is subtract 1 then multiply by 5 The 1st term is 4 Work out the 3rd term.

The term-to-term rule for a different sequence is add 20 then divide by 2 The 2nd term is 50 Work out the 1st term.

A sequence of numbers is formed by the iterative process

Circle 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.

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.

The term-to-term rule for a sequence is

The 3rd term of the sequence is 46 Work out the 1st term. Give your answer as a decimal.

The term-to-term rule for a different sequence is

The 1st term is 34 The 4th term is 10 Work out the value of k.

k =

The term-to-term rule for a sequence is

The first two terms are 2 and 6 Circle the next term.

9 13 14 18

The term-to-term rule for a sequence is

The 1st term of the sequence is 36 Work out the 3rd term.

The term-to-term rule for a different sequence is

The 2nd term of this sequence is 60 Work out the 1st term.

The next term of a sequence is made by adding the previous two terms. Which of these sequences follows this rule? Circle your answer.

–9 2 –7 –5 –12 –3 5 –2 3 1

0 –3 –3 0 –3 –1 –1 –2 –3 1

The term-to-term rule of a sequence is

The first term of the sequence is –24 Work out the next two terms.

The term-to-term rule of a different sequence is

The third term of this sequence is 120 …….. …….. 120 Work out the first term.

Here is a rule for a sequence.

Here is a sequence that follows this rule. 2 10 6 ……. ……. ……. Show that the 6th term is the first one that is not a whole number.

A different sequence follows the same rule. The 1st term is 4 The 3rd term is 9.5 4 ……. 9.5 Work out the 2nd term.

The n th term of a sequence is 12 n – 5 Work out the numbers in the sequence that have two digits and are not prime.

A sequence has three terms. The term-to-term rule for the sequence is multiply by 8 and then add 11

The first term of the sequence is –1 Work out the third term.

The order of the three terms is reversed to make a new sequence. Work out the term-to-term rule for this sequence.