Write the terms of a sequence or a series of diagrams when given the nth term
If you are wondering what is the nth term in maths then you've come to the right place.
A number sequence is just a list of numbers. In maths, this list usually follows a pattern.
We can define this pattern with a mathematical expression.
The 'n^{th} term' is just the n^{th} number in the sequence.
The n^{th} term rule for a sequence tells us what number n will be.
They look something like this:
4n + 6
When we are given the nth term we are able to work out the sequence of numbers that follows this pattern.
Firstly we must look at our nth term rule and take out the information which we will need to help us.
The number infront of n in the nth term rule tells us how much the numbers in our sequence goes up by each time, this is called the termtoterm rule. For our example we know that this is 4 ( 4n + 6 ). So now we know each number goes up by 4 (like the 4 times table).
Since we know that our sequence goes up by 4 we know that it follows the same rule as the 4 times tables. So we can write out the 4 times table which will help us to figure out our sequence!
4, 8, 12, 16, 20, 24, 28 ...
Ok, now looking back out our nth term formula we can now see that our formula is also telling us that we must add 6 to our four times table each time to find our sequence ( 4n + 6 ) . So let's look at the 4 times table again and try and figure out what our sequence will be!
Four times table: 4, 8, 12, 16, 20, 24, 28 ...
+6,+6,+6,+6,+6,+6,+6...
Our sequence: 10, 14, 18, 22, 26, 30, 34 ...
When we line up our sequence with the four times table we can check if our sequence is right!
 We must firstly ask is our term to term rule 4? Check!
 Is our sequence more than the four times table by 6 everytime? Check!
So now we know our sequence is correct by checking it against the rules of our formula!
So lets look back out our nth term formula and conclude what it means:
4n + 6
From our example we now know the following:
 The number infront of n (4) tells us which times tables our sequence follows also called the termtoterm rule.
 The number which comes after the + sign (6) tells us how much our sequence is more than the four times table each time.
Now we understand what our nth term formula means let's try one more example where we are going to write out the terms of a sequence when we are given the nth term.
Example: 8n + 5
 We know that our sequence follows the 8 times table: 8n, so let's write it out.
Step 1: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 ...
 We know that the difference between the 8 times table and our sequence is that of + 5: 8n +5, so let's write out our sequence now
Step 2: 13, 21, 29, 37, 45, 53, 61, 69, 77, 85...
 Now we can double check our sequence by using the formula and finding the 10th term for both the 8 times table and our sequence, which we have already done above by simply writing out the formula.
8n = 8 x 10 = 80
8n + 5 = 8 x 10 + 5 = 85
 Now we can check our 10th terms in our sequences against our answers from the formulas and we can conclude that we have worked out our sequence correctly!
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