Continuing and describing sequences

Here are the first four terms of a sequence.

4   9   14   19

Write down the next two terms.

Here are the first four terms of a sequence.

3    6    12    24

1. Write down the next term of the sequence.
2. Write down the term-to-term rule of the sequence.

In this sequence, each term is found by adding the two terms before it.

2   3   5   8   13

Write down the next two terms.

Here are the first five square numbers.

1    4    9    16    25

1. Write down the next square number after 25.
2. Write down the 8th square number.

Matchsticks are used to make a row of squares.

Pattern 1 (one square) uses 4 matchsticks.
Pattern 2 (two squares) uses 7 matchsticks.
Pattern 3 (three squares) uses 10 matchsticks.

How many matchsticks are used in pattern 6?

Here are the first five terms of a Fibonacci sequence.

2    3    5    8    13

1. Write down the next term of the sequence.
2. Describe the rule for finding the next term of the sequence.

Here are the first five triangular numbers.

1   3   6   10   15

Write down the next two triangular numbers.

Here are the first four cube numbers.

1    8    27    64

1. Write down the next cube number after 64.
2. Write down the 10th cube number.
3. Explain why 200 is not a cube number.

Here are the first four terms of a sequence.

50   44   38   32

1. Write down the next two terms.
2. Work out the first term in the sequence that is negative.

Here are the first four terms of a sequence.

14    11    8    5

1. Work out the next two terms of the sequence.
2. Write down the term-to-term rule of the sequence.

Here are the first four terms of a sequence.

3   8   13   18

1. Zara says 83 is in the sequence. Is she right? Give a reason.
2. Zara says 100 is in the sequence. Is she right? Give a reason.

Here is a sequence.

6   10   14   18   22

Ben says 50 will be in the sequence. Is Ben right? Give a reason.

Here are the first four terms of a sequence.

96    48    24    12

1. Write down the next term of the sequence.
2. Work out the 8th term of the sequence.

The first triangular numbers are 1, 3, 6, 10, 15, 21, ...

Is 45 a triangular number? Show how you know.

The first two terms of a sequence are 3 and x.

Each term after that is the sum of the two terms before it.

The 4th term is 17.

1. Work out the value of x.
2. Work out the 5th term.

Here are the first five triangular numbers.

1    3    6    10    15

1. Describe how the sequence continues from one term to the next.
2. Work out the next two terms of the sequence.

Here are three sequences.

Sequence A:  7    11    15    19

Sequence B:  2    6    18    54

Sequence C:  1    4    5    9    14

1. Write down the letter of the geometric sequence.
2. Work out the next term of sequence C.
3. Work out the 10th term of sequence A.

The even numbers form the pattern

2,  4,  6,  8,  ...

Write down the 12th number in this pattern.

Here are the first three patterns in a sequence made from grey square tiles.

Pattern 1 uses 5 tiles. Pattern 2 uses 8 tiles. Pattern 3 uses 11 tiles.

The number of tiles goes up by the same amount from each pattern to the next.

1. Work out the number of tiles in pattern 5.
2. Write down an expression, in terms of n, for the number of tiles in pattern n.
3. Explain why there is no pattern in this sequence that uses exactly 100 tiles.