Unit 7 Section 2 : Finding the Next Term

In this section, we will use the first few numbers of a sequence to deduce the pattern and hence find the next term.

Example Question

(a) What are the next 3 numbers in the sequence: 12, 17, 22, ... ?

To help us spot the pattern, it is usually helpful to work out the differences between each term, like this:

We can see that each term is found by adding 5 to the previous term, so the 4th term must be 27 (22 + 5 = 27)

What are the 5th and 6th terms?

(b) What are the next 3 numbers in the sequence: 50, 47, 44, 41, 38, ... ?

Again, we find the differences:

This time, each term is found by subtracting 3 from the previous term, so the 6th term must be 35 (38 - 3 = 35)

What are the 7th and 8th terms?

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

IMPORTANT: When a question asks for a list of numbers, you must separate them by commas, like this:

Question 1
Look at the differences in each of these sequences and work out the next three numbers.

(a) 1, 4, 7, 10, 13,
(b) 3, 5, 7, 9, 11,
(c) 5, 8, 11, 14, 17,
(d) 6, 8, 10, 12, 14,
(e) 20, 19, 18, 17, 16,
(f) 6, 9, 12, 15, 18,
(g) 22, 20, 18, 16, 14,

Question 2
Fill in the missing number in each of the sequences below.

(a) 4, 7, , 13, 16, ...
(b) 7, , 15, 19, 23, ...
(c) 8, 14, 20, , 32, ...
(d) 3, 11, , 27, 35, ...
(e) 15, , 27, 33, 39, ...

Question 3
Look at the differences in each of these sequences and work out the next three numbers.

(a) 18, 30, 42, 54, 66,
(b) 4.1, 4.7, 5.3, 5.9, 6.5,
(c) 14, 31, 48, 65, 82,
(d) 101, 119, 137, 155, 173,
(e) 3.42, 3.56, 3.70, 3.84, 3.98,
(f) 10, 9.5, 9, 8.5, 8, 7.5,

Question 4
In each of the parts of this question there is a sequence of patterns. Draw the next two patterns in the sequence on the grid provided, and give the next three numbers in each sequence. To plot points, simply click on the grid provided and a mark will appear. Click again on the same point if you want to remove a particular mark.

(a)  The 4th, 5th and 6th numbers are

(b)  The 5th, 6th and 7th numbers are

(c)  The 5th, 6th and 7th numbers are

(d)  The 5th, 6th and 7th numbers are

Question 5
Find the first number in each of these sequences.

(a) , 6, 11, 16, 21, ...
(b) , 7, 9, 11, 13, ...
(c) , 6, 5, 4, 3, ...
(d) , 19, 28, 37, 46, ...
(e) , 12, 9, 6, 3, ...

Question 6
Work out the next three numbers in each sequence below.
Be careful - the differences between each term may not be constant.

(a) 1, 4, 9, 16, 25,
(b) 2, 5, 10, 17, 26,
(c) 0, 3, 7, 12, 18,
(d) 6, 12, 20, 30, 42,
(e) 0.5, 2.0, 4.5, 8.0, 12.5,

Question 7
Fill in the missing number in each of the sequences below.

(a) 2, 4, , 16, 32, ...
(b) 100, 81, 64, , 36, ...
(c) 6, 9, , 21, 30, ...
(d) 0, 1.5, 4, , 12, ...
(e) 1, 7, 17, , 49, ...

You have now completed Unit 7 Section 2
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