# VR - Negative Arithmetic Progression and Adding Consecutive Numbers

## Negative Arithmetic Progression

Use the following series of numbers to determine what should come next.

 50 42 34 26

To get from the first number to the second you must subtract eight. This carries through for each number so the answer will be 26 - 8 = 18.

There are all sorts of variations with this question - some of these crop up later - but the majority of the time the first of its sort in a test paper will follow this straightforward style.

Technique tip:

Look out for the use of negative numbers - they may appear already in the sequence as the final number or the answer may be a negative number despite there having been none in the sequence. It's very common practise for the multiple choice answers to include both the (correct) negative number and the same digit but without the ' - ' sign in front of it. This is a trick to catch out the unwary and often children misread and tick the wrong box. I don't think we should be trying to punish those who are rushing through a tough exam and don't notice the tiny minus sign, but that's the way of things - warn your child in advance to check for things like that.

Use the following series of numbers to determine what should come next.

 4 8 12 20 32

This is a tricky style of progression as it does not rely on a simple arithmetic or geometric progression. It is one of the hardest types for children to spot and there is often one of this kind at the end of a section. Ensure your child recognises it!

Technique tip:

The technique I teach for all of these questions is to write down the difference between each number and work from there. It may not provide the answer but it will often help.

If we follow that then it will look something like this:

 4 4 8 12 4 8 12 20 32

This technique allows a child to see if there is a clear progression but of course it doesn’t aid us greatly unless your son or daughter notices that there is a repeat of 4, 8, 12 in the differences between the numbers and the series itself. Using this information you should add 20 to the last number as this would keep the top sequence running parallel to the main series. That’s the awkward way of doing it but your child may like it. However, the simple way is to approach it with the knowledge of ways to create a series. Here, it’s the adding of consecutive numbers. 4 +8 = 12, 8 + 12 = 20 and so on. The answer will be 20 + 32 = 52.

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