What do 'nth' and 'nth term' mean in maths?

When you're describing how to get somewhere you might tell someone to 'go up the 5th street on the left'. This just means go past the first four, and go up the next one. When choosing an item of clothing from a rail, you might say 'the 7th one along'. This just means count along 7 and pick that one.

If I wanted to simplify that description of how to find the 5th road, or the 7th item of clothing (or even the 18th bottle on the wall, the 48th marble in the bag or the 239th name on a list), I might say something like this:

"To find the nth object, just count along the objects until you get to n."

This might look more complicated at first, but think about what it means: In maths, we can use a letter to:

1. represent numbers we don't know yet, or
2. work as place holder for something that works with any number.

In the example above, it's the second case that works for us. We could swap any number for n, and the statement would still make sense:

"To find the 5th object, just count along the objects until you get to 5."
"To find the 8th object, just count along the objects until you get to 8."
"To find the 846th object, just count along the objects until you get to 846.

What's the point?
In the example above, it may seem a little pointless, but remember that this is an over-simplified example. A slightly more complicated example is:

Imagine that a shop sells sea shells. The price of the shells is three for £1. The shop keeper could say, then, that:

"The number of sea shells I give a customer is three times the number of pounds the customer gives me."

Using our notation, we can write down the number of shells that he'd have to give his customer with a bit less effort. If the customer gives £n, then he gets 3 x n shells in return. If you can remember that 'n' stands for the number of pounds the customer gives, then remembering (and writing) "3 x n" takes a lot less effort than remembering "multiply the number of pounds by 3".


What about 'nth term'?
The 'nth term' is to do with sequences. A sequence is basically a list of numbers that follows some kind of rule. If you'd like to know more about sequences, please leave a comment and ask!

Take the following sequence as an example:

5, 8, 11, 14, 17, 20, 23, 26, 29... and so on.

This sequence goes on forever, and writing the whole thing down would take us just as long. We could just say "the sequence starts at 5, then you add three on each time." Or you could write it in the following way:

3n + 2

Then, if you wanted to find the 1st number in the list, you'd just say that n = 1 (3 x 1 + 2 = 5: it works!). If you wanted to find the 2nd, then n = 2 (3 x 2 + 2 = 8: that works too!).
The beauty of writing it down in this way is that you could also skip straight to finding the 48th number in the list: n would be replaced by 48 (3 x 48 + 2 = 146).
Writing down a sequence in this way is called writing down the 'nth term rule'. That just means that if we know which number term* we want to find (for example, the 8th, the 17th or the 4,243rd), we just swap n for that number




* A 'term' is just a posh word for each number in the list. For example, the first 'term' in the sequence we're looking at here is 5. The 7th 'term' in this sequence is 23: it's just the 7th number along when you write the whole list out.