Sequences

The n th term of a sequence is 4 n – 1

Work out the 3rd term of the sequence.

Here are the first four terms of a different sequence. 9 15 21 27

Is 63 a number in this sequence? You must give a reason for your answer.

Here are the first four even numbers. 2 4 6 8 Find the 10th even number.

Here are the first five terms of a quadratic sequence. 3 20 47 84 131

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

The terms of a different sequence are given by the rule u_{n+ 1} = ku_n + k where k is a constant. Given that u₁ = 9 and u₂ = 4

find the value of u₄

Here are the first four terms of a number sequence. 97 91 85 79

Explain how to work out the next number of the sequence.

Work out the difference between the 5th term and the 7th term of the sequence.

Explain why 52 is not a number in this sequence.

Here are the first five terms of a sequence. 3 8 13 18 23

Write down the next term of this sequence.

Write down the ratio of the second term to the fourth term. Give your ratio in its simplest form.

Here are the first five terms of an arithmetic sequence. 7 13 19 25 31

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

The nth term of a different sequence is 8 − 6n

Is −58 a term of this sequence? You must show how you get your answer.

Here are the first five terms of an arithmetic sequence. 7 13 19 25 31

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

The nth term of a different sequence is 8 − 6n

Is −58 a term of this sequence? You must show how you get your answer.

Here are the first three terms of a sequence. 20 16 13

Write down two numbers that could be the 4th and 5th terms of this sequence.

Write down the rule you used to get your numbers.

Here is a sequence of patterns made from grey square tiles.

number 1 number 2 number 3 number 4

On the grid below, draw Pattern number 5

Complete the table.

Here are the first five terms of a number sequence. 3 8 13 18 23

Write down the next two terms of this sequence.

Jim says that 50 is a term in this sequence. Jim is wrong.

Explain why.

The profit made by a shop increases each year. The profit made by the shop in year n is £P_n Given that the profit made by the shop in the next year is £P_{n+ 1} then

The table shows the profit made by the shop in 2018 and in 2019

Work out the profit predicted to be made by the shop in 2021

A number sequence starts 1 2 4 Emma says that the next term is 7

Explain why Emma may be correct.

Here are the first four terms of the sequence of triangle numbers. 1 3 6 10

Find the 8th term of this sequence.

Here are the first five terms of a number sequence. 45 40 35 30 25

Write down the next two terms of this sequence.

A term of this sequence is −5

Which term?

The nth term of a different sequence is given by the expression 4n+ 3

Find the 9th term of this sequence.

The first term of a sequence of numbers is 24 The term-to-term rule of this sequence is ‘add 8’ Josie says, “No number in this sequence is in the 5 times table.”

Give an example to show that Josie is wrong.

Is 85 a number in this sequence? Give a reason for your answer.

The n th term of a sequence is 3 n + 4

Explain why 21 is not a term of this sequence.

Here are the first three terms of a different sequence.

1 2 4

Write down two numbers that could be the 4th term and the 5th term of this sequence. Give the rule you have used to get your numbers.

Here are the first 4 terms of a sequence.

2 9 16 23

Write down the next term in the sequence.

Explain how you got your answer.

Work out the 10th term of the sequence.

The nth term of a sequence is given by an² + bn where a and b are integers.

The 2nd term of the sequence is –2 The 4th term of the sequence is 12

Find the 6th term of the sequence.

Here are the first five terms of a different quadratic sequence.

0 2 6 12 20

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

Here are the first four terms of a number sequence.

2 5 11 23

The rule to continue this sequence is

multiply the previous term by 2 and then add 1

Work out the 5th term of this sequence.

How many square tiles are needed to make pattern number 6?

How many circular tiles are needed to make pattern number 20?

Derek says,

“When the pattern number is odd, an odd number of square tiles is needed to make the pattern.”

Is Derek right? You must give reasons for your answer.