Ok, so here is a sequence:
45, 42, 39, 36
Say we wanted to find a specific "term" of the sequence - e.g. the 10th term or the 100th term. We call this variable the nth term.
This is the formula for finding the nth term:
a + (n - 1)d
Where a = the value of the first term,
And d = the difference between each term.
In our sequence, a = 45 and d = -3.
This is because the first term is 45 and the difference between one term and the next is 3. However, the numbers are getting smaller, so this would be -3.
Now we substitute a and d into the formula to make:
45 + (n - 1) x -3.
We then expand the brackets (see my post or look it up) to make:
45 - 3n + 3
This simplifies to form:
- 3n + 48.
We can check this by substituting n into the formula. n can be any number, but let's say it's 10.
First we multiply 10 by -3, which gives -30.
Then we add 48 - this comes to 18.
Let's check our answer:
1 2 3 4 5 6 7 8 9 10
45 42 39 36 33 30 27 24 21 18.
(if you are on a mobile phone or tablet, we apologise that you may not be able to view this properly. Please use a laptop to view.)
And, just like we predicted, our 10th term is 18.
Don't forget that each sequence has its own formula and that n can be any number. Test your knowledge with this quick quiz:
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