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In this activity, we will learn how to find the formula for the general term Tn of a sequence.
Example
Term number n = 1 2 3 4 5
Term, Tn= 4 8 12 16 20
The common difference is +4
The common difference between the terms is +4, so we write this as 4n.
It is clear, that Tn = 4n.
Compare this sequence with the one below:
Term number n = 1 2 3 4 5
Term, Tn= 7 11 15 19 23
The common difference is +4
The common difference of +4 gives us 4n again.
But this time, we need to do something more.
If we test out 4n with the first term in the table, we get 4 x 1 = 4 but the first term isn't 4, it is actually 7!
This means that we need to do an adjustment to the formula: 7 - 4 = 3, so we know that we need to add 3 to the answer of 4n.
This gives us the corrected formula of 4n + 3
To finish off, we need to test that formula out with some of the other terms to make sure it works:
n = 2 4 x 2 = 8 + 3 = 11, which is correct.
n = 3 4 x 3 = 12 + 3 = 15, which is also correct!
So Tn = 4n + 3
It's a bit tricky, but we'll take it step by step and work through the questions carefully.
Let's get started!
Question
/ 10Mr Shepherd
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Teacher explanation