Sequences

Gabriela designs the seating layout for a new theatre.

• There are 12 seats in the front row.
• Each row has 2 more seats than the row in front of it.

There are 152 seats in the theatre in total.

Work out the number of rows in the theatre.

......................................... rows 

A road has 349 houses on it numbered from 1 to 349.
The diagram shows some of these houses.
The houses on the West side of the road have odd numbers.
The houses on the East side have even numbers.

Tomaz delivers a leaflet to every house on the West side of the road.
He starts at house number 1 and then delivers to each house in order.

Find an expression, in terms of , for the house number of the th house he delivers to.

Alicia delivers a leaflet to every house on the East side of the road.
She starts at house number 348 and then delivers to each house in order.

Find an expression, in terms of , for the house number of the th house she delivers to.

The grid shows the first three diagrams in a sequence.

Each diagram is made using small squares that are white or grey.

On the grid, draw Diagram 4.

Write down the term to term rule for the number of grey squares.

Diagram number	1	2	3	4
Number of small white squares	1	4	9
Number of small grey squares	3	5	7
Total number of small squares	4	9	16

Complete the table.

Work out the number of small white squares in Diagram 18.

One of the diagrams has a total of 900 small squares.

Work out its Diagram number.

Diagram ................................................. 

Another diagram has 43 small grey squares.

Work out the total number of small squares in this diagram.

Here is a sequence of numbers.

3,   6,   11,   18,   27,   ...

Find an expression for the nth term of this sequence.

The grid shows the first three diagrams in a sequence.

Each diagram is made using identical small squares.

Each square has sides that are 1 unit long.

These are the first four diagrams in a sequence.

Each diagram is made from small equilateral triangles.

Mrs Verma has a restaurant.
In the restaurant each table has 8 chairs.
Sometimes she puts tables together.
The diagrams show how the tables are put together and the position of each chair (X).

The pattern of tables and chairs forms a sequence.

Draw the diagram for 4 tables.

Complete the table.

Find a formula for the number of chairs, c, in terms of the number of tables, t.

c = ............................... 

18 tables are put together in this way.

Work out the number of chairs needed.

Work out the number of tables, put together in this way, when 80 chairs are needed.

These are the first four terms of a sequence.

11         15            19                 23

Write down an expression for the th term.

[2]

Each of 196 candidates has a candidate number from 3001 to 3196.

The candidates sit in numerical order in columns and rows, as shown in the diagram.

There are 20 rows.

The diagram shows part of the plan for where the candidates sit.

The diagram shows where candidates  and  sit.

Write down their numbers.

..................................      
..................................  [2]

A sequence of patterns is made using lines and dots.
The first three patterns in the sequence are shown below.

Draw Pattern 4 on the grid.

Complete the table.

Find an expression, in terms of , for

the number of dots in Pattern ,

A pattern has 76 lines.
Work out how many dots are in this pattern.

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

                   ....

These are the first five terms in a sequence.

8          11             14                17                 20

Find the next term.

Find an expression for the th term.

Write down an expression for the nth term of this sequence.

1             8             27              64

The th term of a sequence is 60-8.

Find the largest number in this sequence.

Here are the first five terms of a different sequence.

Find an expression for the th term of this sequence.

The th term of a sequence is .

These are the first four terms of a sequence.

27      33      39      45

Find the nth term of this sequence.

Here are the first three patterns in a sequence.

These are the first four terms of a sequence.

Write down the next term.

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

These are the first five terms of a sequence.

-4        2         8          14            20

Find an expression for the th term of this sequence.

These are the first four terms of a sequence.

8            15             22             29

[1]

Find an expression for the th term of this sequence.

[2]

Here are the first four terms of a sequence.

3      9      15      21

Find the first three terms of the sequence with th term .

These are the first four terms of a sequence.

The th term of a sequence is 

Find the first three terms of this sequence.