GCSE Maths · Higher · Chapter 4: Number and sequences · Lesson 1

Sequences and the nth term

Grades 4–6About 45 minutesNo calculator35 marks

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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Work out $3 x^{2} + 5$ when $x = - 3$ .
[1 mark]
Answer
A2
From chapter 2
Work out $\frac{3}{4} \times \frac{2}{9}$ in its simplest form.
[1 mark]
Answer
A3
Last lesson
What type of correlation would you expect between outside temperature and heating bills?
[1 mark]
Answer
A4
Key Stage 3
Work out $0.7 \times 5$ .
[1 mark]
Answer

Grades 4–5

Your teacher works through each example with you. Then try the one beside it.

Example 1

Find the $n$ th term of the sequence $4$ , $10$ , $16$ , $22$ , ...

Hint They go up by

6

: compare with

6 n

B1
Find the $n$ th term of the sequence $3$ , $14$ , $25$ , $36$ , ...
[2 marks]
Answer

Example 2

The $n$ th term is $6 n + 4$ . Is $150$ a term? Find the first term greater than $150$ .

Hint Solve

6 n + 4 = 150

: is

n

whole?

B2
The $n$ th term is $8 n - 5$ . Is $125$ a term? Find the first term greater than $125$ .
[3 marks]

Grades 4–6

C1
Write down the first three terms of the sequence with $n$ th term $11 - 4 n$ .
[2 marks]
Answer
C2
Find the $n$ th term of the sequence $47$ , $42$ , $37$ , $32$ , ...
[2 marks]
Answer

C3
Which term of the sequence with $n$ th term $3 n + 11$ is equal to $95$ ?
[2 marks]
Answer
C4
Write down the next two terms of the sequence $2$ , $5$ , $11$ , $20$ , ...
[2 marks]
Answer
C5
The $4$ th term of a linear sequence is $31$ and the $11$ th term is $87$ . Find the $n$ th term.
[3 marks]
Answer
C6
Sequence $A$ has $n$ th term $5 n + 17$ . Sequence $B$ has $n$ th term $8 n - 4$ . Find the position at which the two sequences have the same term, and that term.
[3 marks]
Answerposition $\dots\dots$ , term $\dots\dots$

Grades 5–6

D1
The $n$ th term of a sequence is $6 n - 1$ . Sam says, "Every term of this sequence is odd, so $85$ must be a term."
Show that Sam is wrong.
[2 marks]

Grade 7 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can continue a sequence and write down terms from an $n$ th term rule.
I can find the $n$ th term of a linear sequence.
I can use the $n$ th term to decide whether a number is a term and to find the first term past a value.

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