New
New
Year 8

# Calculating any term

I can calculate any term using the n^th term.

New
New
Year 8

# Calculating any term

I can calculate any term using the n^th term.

## Lesson details

### Key learning points

1. The position to term rule can be expressed using n.
2. A sequence can be generated using successive values of n .
3. Any term can be calculated using the n^th term.

### Common misconception

That the sequence $$3n+2$$ starts with 3 and adds 2, or starts with 2 and adds 3.

Calculate the first few terms. Ask, "When $$n = 1$$ what is the term value?" This is the first value for our sequence.

### Keywords

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

Discuss the misconceptions very openly. Ask questions like, "What does the sequence $$8n+23$$ begin with? Is it 8? 23? 31?". Address why it is 31. This will also help future learning on finding $$n$$^th terms.
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 of these words is also used to describe an arithmetic sequence?
Positive.
Geometric.
Q2.
Which is the simplified version of $$2 \times a + 5 \times b + 3$$?
Correct answer: $$2a+5b+3$$
$$7ab+3$$
$$10ab$$
It is already in it's simplest form.
Q3.
If $$a=5$$ and $$b=7$$ what is the value of the expression $$2a+5b+3$$?
25 + 57 + 3
85
42
Q4.
When $$n=5$$ what is the term value?
$$T=5$$
$$n=2$$
2
Correct answer: $$T=11$$
+2
Q5.
Evaluate the expression $$70-3x$$ when $$x=50$$.
20
-30
-50
220
Q6.
Given that $$a=9$$. $$b=-7$$. Put these expressions in order from lowest to highest value.
1 - $$3b-5a$$
2 - $$5(a+3b)$$
3 - $$-5a-3b$$
4 - $$5a+3b$$
5 - $$5a-3b$$

## Exit quiz

### 6 Questions

Q1.
The $$n^\text{th}$$ term can be used to calculate any term in a sequence so we can call it a __________ for finding the $$n^\text{th}$$ term.
equation
sequence
term value
Q2.
If the $$n^\text{th}$$ term is $$3n+7$$ what are the first five terms?
3, 10, 17, 24, 31, ...
7, 10, 13, 16, 19, ...
10, 17, 24, 31, 38, ...
Correct answer: 10, 13, 16, 19, 22, ...
Q3.
What is the 5$$^\text{th}$$ term of $$0.3n + 0.07$$?
0.37
2.2
1.75
5.37
Q4.
What are the first five terms of $$10-2n$$?
10, 8, 6, 4, 2, ...
12, 10, 8, 6, 4, ...
Correct answer: 8, 6, 4, 2, 0, ...
-2, -4, -6, -8, -10 ...
Q5.
Order these term values from lowest to highest.
1 - The 50$$^\text{th}$$ term of the sequence $$2n-1$$.
2 - The 15$$^\text{th}$$ term of the sequence $$6n+10$$.
3 - The 101$$^\text{st}$$ term of the sequence $${1 \over 2} n + 50$$.
4 - The 9$$^\text{th}$$ term of the sequence $$200-11n$$.
Q6.
Which statements are true for the arithmetic sequence $$1.25n-0.3$$?
The sequence contains the number 1.25
Correct answer: The sequence contains the number 2.2
The sequence goes down by 0.3 each time.
Correct answer: The sequence goes up by 1.25 each time.
Correct answer: The sequence starts at 1.25-0.3