Identify these questions

We’ve looked at number series where numbers go up, down or alternate and learnt how to detect patterns when we see these questions.

But, sometimes, there are tricky questions where the gaps are quite large and where your standard operators (addition, subtraction, division and multiplication) may not provide you with the pattern quickly.

They’re questions that look like this:

What is the next number in this series?

1, 4, 9, 16, 25, 36

A 45 B 47 C 49 D 56

OR,

The numbers in each pair of brackets follow the same rule.

Find the missing number.

[2, 4] [11, 121] [?, 36] [4, 16]

A 3 B 4 C 6 D 9

They’re characterised by really large gaps between numbers where an obvious pattern cannot be easily found using simple multiplication / addition / division or subtraction.

Now that you can identify them, let’s see how to find the underlying pattern and solve them.

The strategy to answer these questions

To answer these questions, you will be required to:

1. Identify the relationship (this relationship or pattern will hold true for all the numbers) between the numbers, and,
2. Use that relationship to find the missing number or the grouped number set.

Here are rules to uncovering the pattern when there are large gaps (up / down) in between numbers:

• Look at exponentials or surds for numbers in order index. For example, 2 squared (2 x 2), 2 cubed (2 x 2 x 2) or square root 121, square root 100 etc….
• Look at exponentials for previous number multiplied by itself to get to the subsequent number or previous number to the power of the order index.
• Failing the above, check to see if exponentials or surds could be combined with any of the other four operators.

Example Question/s

Watch video for explanation of the following question/s:

What is the next number in this series?

1, 4, 9, 16, 25, 36, ?

A 45 B 47 C 49 D 56

The numbers in each pair of brackets follow the same rule.

Find the missing number.

[2, 4] [11, 121] [?, 36] [4, 16]

A 3 B 4 C 6 D 9

What is the next number in this series?

100, 81, 64, 49, 36, ?

A 19 B 20 C 25 D 29

Key Rules to remember

• Large gaps in between numbers may require a different approach – try exponentials or surds.
• Exponentials or surds can be based on the order number
• Exponentials or surds can use existing numbers to create subsequent numbers
• Exponentials or surds can be combined with other operators

Practice time!

Now, it's your turn to practice.

Click on the button below and start your practice questions. We recommend doing untimed mode first, and then, when you're ready, do timed mode.

Every question has two solutions videos after you complete the question. The first is a quick 60 second video that shows you how our expert answers the question quickly. The second video is a more in-depth 5-steps or less explainer video that shows you the steps to take to answer the question. It's really important that you review the second video because that's where you'll learn additional tips and tricks.

Once you're done with the practice questions, move on to the next checkpoint.

Now, let’s get started on your practice questions.

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