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What is the nth term?... Like what is it?, How do I find it?, and how exactly is used?... I'm a grade 11 student in a advanced grade 12 mathematics class, I have yet to take a grade 11 mathematics course, and I'm stuck.
 

 

Hi Alex,

By "the nth term" of a sequence we mean an expression that will allow us to calculate the term that is in the nth position of the sequence. For example consider the sequence

2, 4, 6, 8, 10,...

The pattern is easy to see.

    1. The first term is two.
    2. The second term is two times two.
    3. The third term is two times three.
    4. The fourth term is two times four.
    5. The tenth term is two times ten.
    6. the nineteenth term is two times nineteen.
    7. The nth term is two times n.

In this sequence the nth term is 2n.

What about this one?

3, 9, 27, 81,...

Here the terms are

3 = 31
9 = 32
27 = 33
81 = 34

In this case the nth term is 3n .

Sometimes it is not as easy to find an expression for the nth term

5, 13, 33, 89,...

I got this by adding the two sequences above

5 = 2 + 3, 13 = 4 + 9, 33 = 6 + 27, 89 = 8 + 81,...

Now that you see it you can write the nth term. It is 2n + 3n.

Penny

 
 

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