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Use the nth Term in this Sequence

In this worksheet, students use the nth term to decide if a number is in a given sequence.

'Use the nth Term in this Sequence' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Algebra

Curriculum subtopic:   Sequences

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

One of the most common follow up questions when you are dealing with a sequence is 'Is the number X in this sequence?'.

There are a couple of ways to do this.

 

Method 1:The easy spot.

There are sometimes really easy ways to do this.

Example 1: Is the number 275 in the sequence 4, 8, 12, 16, 20....

You should straight away spot that 275 is off and all the numbers in the sequence are even, so it can't be in the sequence.

Example 2: Is the number 97 in the sequence 3. 8. 13. 18. 23...

This one is a bit trickier. Did you notice that all the numbers in the sequence end in 3 or 8? 97 can't be in the sequence.

 

Method 2: Using the Nth term.

To use this, we have to remember that n in the nth term is the position. You can't have a number in the 1.5th position.

Example 3: Is 75 in the sequence 2, 5, 8, 11...

Step 1: Find the nth term of the sequence.

For our sequence this would be 3n - 1

Step 2: Make this nth term equal to the number you are looking for (in this case 75) and then solve the equation

3n - 1 = 75

3n = 76

n = 25.3333

Because n isn't a whole number, 75 cannot be in the sequence

 

Example 4: Is 224 in the sequence 8, 14, 20, 26...

Step 1: Find the nth term of the sequence.

For our sequence this would be 6n + 2

Step 2: Make this nth term equal to the number you are looking for (in this case 224) and then solve the equation

6n + 2 = 224

6n = 222

n = 37

Because n is a whole number, 224 is in the sequence

 

Is a given value is in a sequence, the value of n must be an....

38 is in the sequence 3n + 2. What position is it in?

43 is in the sequence 5n - 7. What position is it in?

Is 24 in the sequence 3, 8, 13, 18...

Yes

No

Is 273 in the sequence 2, 6, 10, 14

Yes

No

Is 33 in the sequence 2n + 5?

Yes

No

Match the nth term with the number that appears its sequence.

Column A

Column B

4n + 1
153
3n - 7
29
2n + 3
201

For each of these nth terms, select if the number in the bracket is (Y) or is not (N) in the sequence.

Check the number that are in the sequence 3n - 1

8

17

21

26

32

40

Complete the following sentence...

8

17

21

26

32

40

  • Question 1

Is a given value is in a sequence, the value of n must be an....

CORRECT ANSWER
EDDIE SAYS
We know that for this to happen. N must be a whole number. The correct language to use here is that N is an integer.
  • Question 2

38 is in the sequence 3n + 2. What position is it in?

CORRECT ANSWER
12
EDDIE SAYS
Start by setting this up as an equation. 3n + 2 = 38 All we have to do is now solve this for N.
  • Question 3

43 is in the sequence 5n - 7. What position is it in?

CORRECT ANSWER
10
EDDIE SAYS
Start by setting this up as an equation. 5n - 7 = 43 All we have to do is now solve this for N.
  • Question 4

Is 24 in the sequence 3, 8, 13, 18...

CORRECT ANSWER
No
EDDIE SAYS
All the number in the sequence end in 3 or 8 so 24 cannot be in the sequence.
  • Question 5

Is 273 in the sequence 2, 6, 10, 14

CORRECT ANSWER
No
EDDIE SAYS
All the number in the sequence are even and 273 is odd
  • Question 6

Is 33 in the sequence 2n + 5?

CORRECT ANSWER
Yes
EDDIE SAYS
We start by setting up the equation. 2n + 5 = 33 Id we solve this, do we get a whole number for N?
  • Question 7

Match the nth term with the number that appears its sequence.

CORRECT ANSWER

Column A

Column B

4n + 1
201
3n - 7
29
2n + 3
153
EDDIE SAYS
It's a bit of a process of elimination here. I'd start with the ones that look similar (4n + 1 and 201 both end in 1), test that and move on when you've decided.
  • Question 8

For each of these nth terms, select if the number in the bracket is (Y) or is not (N) in the sequence.

CORRECT ANSWER
EDDIE SAYS
This is just a case of setting the equations up and solving them to find N. i.e. 2n + 1 = 10 gives n = 4.5 so it isn't in the sequence.
  • Question 9

Check the number that are in the sequence 3n - 1

CORRECT ANSWER
8
17
26
32
EDDIE SAYS
You need to work carefully here, you could use the nth term method, but it's easier here just to write out the sequence. 2, 5, 8, 11, 14, 17... It's quicker to spot the number.
  • Question 10

Complete the following sentence...

CORRECT ANSWER
EDDIE SAYS
As we said, you need to make the number you are looking for equal to the nth term and solve for N If N is an integer, it\'s in the sequence.
---- OR ----

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