 # Generate a Sequence from an nth Term

In this worksheet, students practise generating a sequence from an nth term. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Algebra

Curriculum subtopic:   Sequences

Difficulty level:   ### QUESTION 1 of 10

One of the questions that catches students out a lot when they are dealing with sequences is generating a sequence from an nth term.

To deal with this, we have to remember what an nth term is actually for. It is a position to term rule that allows the position within the sequence to give us the number in the sequence.

Example 1: Find the first 5 terms in the sequence 4n - 6

For this, we have to substitute in the values n = 1, n = 2, n = 3, n = 4 and n = 5 into the nth term.

When n = 1, 4n - 6 = (4 x 1) - 6 = -2

When n = 2, 4n - 6 = (4 x 2) - 6 = 2

When n = 3, 4n - 6 = (4 x 3) - 6 = 6

When n = 4, 4n - 6 = (4 x 4) - 6 = 10

When n = 5, 4n - 6 = (4 x 5) - 6 = 14

So our first five terms for the sequence 4n - 6 are -2, 2, 6, 10, 14

Example 2: Find the difference between the 100th and the 90th terms in the sequence 5n + 2

The approach to this is very similar to the last question but we use n = 90 and n = 100

When n = 100, 5n + 2 = (5 x 100) +2 = 502

When n = 90, 5n + 2 = (5 x 90) +2 = 452

We can then find the difference by subtracting the two values. 502 - 450 = 50

Complete the following sentence.

What are the first five terms of 2n - 3

What are the first 5 terms for 3n + 2?

What is the 100th term in the sequence given by 3n - 5?

James says that the 4th term of 3n - 1 is one third of the 4th term of 7n +5.

Is he correct?

Yes

No

What is the difference between the 100th and 50th numbers in the sequence 5n - 1

Match the sequence with the correct first 5 terms.

## Column B

2n + 1
5, 9, 13, 17
3n - 2
1, 4, 7, 10, 13
4n + 1
3, 5, 7, 9, 11
6n - 7
-1, 5, 11, 17, 23

Which number appears in both the sequences described by 2n + 1 and 4n + 1?

What is the average of the first 5 terms of 7n - 3?

Which is larger?

The 12th term of 3n + 2 or the 6th term of 6n + 1

12th term of 3n + 2

6th term of 6n + 1

They're the same

• Question 1

Complete the following sentence.

EDDIE SAYS
It's important to use the correct vocab. When we change a letter into a number in algebra, this is called substitution so we substitute the number
• Question 2

What are the first five terms of 2n - 3

EDDIE SAYS
Remember we are just going to substitute the numbers 1 to 5 in for n. For example When n = 3, 2n - 3 = (2 x 3) - 3 = 3
• Question 3

What are the first 5 terms for 3n + 2?

EDDIE SAYS
Remember we are just going to substitute the numbers 1 to 5 in for n. For example When n = 3, 3n + 2 = (3 x 3) + 2 = 11
• Question 4

What is the 100th term in the sequence given by 3n - 5?

295
EDDIE SAYS
All we have to do here is substitute n = 100 into the nth term. Same as before, just a bigger number.
• Question 5

James says that the 4th term of 3n - 1 is one third of the 4th term of 7n +5.

Is he correct?

Yes
EDDIE SAYS
Lets split the question up. The 4th term of 3n - 1 is (3 x 4) - 1 = 11 The 4th term of 7n + 5 is (7 x 4) + 5 = 33 Is 11 one third of 33?
• Question 6

What is the difference between the 100th and 50th numbers in the sequence 5n - 1

250
EDDIE SAYS
Did you spot that this is like one of the examples in the intro? We need to find the 100th term and the 50th term and then subtract them
• Question 7

Match the sequence with the correct first 5 terms.

## Column B

2n + 1
3, 5, 7, 9, 11
3n - 2
1, 4, 7, 10, 13
4n + 1
5, 9, 13, 17
6n - 7
-1, 5, 11, 17, 23
EDDIE SAYS
Do you even need to work these all out? 2n + 1 must go up in 2s. Which one does it have to be?
• Question 8

Which number appears in both the sequences described by 2n + 1 and 4n + 1?

9
EDDIE SAYS
The only way we can do this is to work out the sequences. 2n + 1 3, 5, 7, 9, 11 4n + 1 5, 9, 13, 17, 21 Which number is in both?
• Question 9

What is the average of the first 5 terms of 7n - 3?

18
EDDIE SAYS
The first step is to work out the sequence. 7n - 3 = 4, 11, 18, 25, 32 If you just see the word average, remember that it is the mean you are using. Add them all up and divide by how many there are. 90 ÷ 5 = 18
• Question 10

Which is larger?

The 12th term of 3n + 2 or the 6th term of 6n + 1

12th term of 3n + 2
EDDIE SAYS
This looks harder than it actually is. All we need to do is to work them out the same way as before and compare them. 12th term of 3n + 2 = (3 x 12) + 2 = 38 You do the rest.
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