New
New
Year 8

# Problem solving with sequences

I can use my knowledge of sequences to solve problems.

New
New
Year 8

# Problem solving with sequences

I can use my knowledge of sequences to solve problems.

## Lesson details

### Key learning points

1. Patterns can be described using sequences.
2. Sequences can be found for given terms even if they are not sequential .
3. It is possible to identify which term in a sequence a number is from the rule.
4. Real life sequences can be represented on a graph.

### Common misconception

The answer to the 'handshake' problem is 15, or 15x15

Group pupils into 3s and ask them to record how many handshakes are made. Then group as 4s and repeat. What do they notice?

### Keywords

• Arithmetic sequence - An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a constant.

• Nth term - The nth term of a sequence is the position of a term in a sequence where n stands for the term number.

Encourage pupils to play with the problems and test their hypotheses rather than answering yes/no when asked if an hypothesis is correct. This encourages pupils to be resilient learners and test their ideas.
Teacher tip

### Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Starter quiz

### 6 Questions

Q1.
Which words would describe the sequence 1,4,9,16,25, ...?
Arithmetic
Linear
Q2.
What is the next term in the arithmetic sequence starting -19,-12,-5,2 ...
5
7
11
Q3.
Buses leave for Finchley Park every 25 minutes. If a bus just left at 7:41 am what time will the next bus leave?
8:56 am
8:66 am
8:16 am
Correct answer: 8:06 am
Q4.
What is the $$n^\text{th}$$ term of the arithmetic sequence 8,9,10,11, ...?
$$n+8$$
$$8+n$$
$$8n$$
Correct answer: $$n+7$$
$$n+9$$
Q5.
What is the $$n^\text{th}$$ term of the arithmetic sequence 8,11,14,17 ...?
$$n+3$$
$$8n+3$$
$$3n+8$$
$$3n+11$$
Correct answer: $$3n+5$$
Q6.
The 118$$^\text{th}$$ term of the sequence $$5050-7n$$ is 4224. What is the 113$$^\text{th}$$ term?
4266
4252
4182
4189

## Exit quiz

### 6 Questions

Q1.
Which would describe the sequence 1,3,6,10,15, ...?
Arithmetic
Linear
Q2.
The 2$$^\text{nd}$$ term of an arithmetic sequence is 11 and the 6$$^\text{th}$$ term is 47. What is the 1$$^\text{st}$$ term of the sequence?
0
1
3
4
Q3.
Buses leave Wallsend for Byker at regular intervals. The second bus of the day leaves at 6:44 am. You just missed the seventh bus of the day which left at 8:04 am. What time is the next bus?
8:14 am
Correct answer: 8:20 am
8:24 am
8:30 am
8:34 am
Q4.
The 24$$^\text{th}$$ term of an arithmetic sequence is 281. The 37$$^\text{th}$$ term is 437. Which calculation will be the starting point to finding the $$n^\text{th}$$ term of the sequence?
Correct answer: $${437 - 281}\over{37-24}$$
$${437 - 281}\over{24-37}$$
$${281 - 437}\over{37-24}$$
$${37-24}\over{437 - 281}$$
$${24-37}\over{437 - 281}$$
Q5.
What is the $$n^\text{th}$$ term of this sequence?
$${n+7} \over {n+5}$$
$${7n+2} \over {5n+3}$$
$${7n+5} \over {5n+2}$$
Correct answer: $${7n-5} \over {5n-2}$$
It's not an arithmetic (linear) sequence we can't write an $$n^\text{th}$$ term.
Q6.
How many triangles are there in this pattern? Don't forget to count all triangles of all sizes.
50