In an arithmetic sequence like this:
4, 10, 16, 22, 28, 34 ...
the nth term is found as follows:
Step 1
Find the common difference between the terms.
Here it is 6.
Step 2
The common difference is the coefficient of n.
Here we get 6n.
Step 3
Compare this to the actual sequence and adjust the formula by adding or subtracting a fixed number.
Here 6n would give us the terms 6, 12, 18, 24, 30 etc. ... which is 2 more than our sequence of 4, 10, 16, 22, 28 etc.
So we must subtract 2.
So the nth term is 6n - 2.
We can test this by putting in n = 5 to check that the 5th term is really 28.
It is because 6 × 5 - 2 = 30 - 2 = 28.
Let's try some questions now.
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