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Hi Jesse.

There are two common kinds of sequences: arithmetic and geometric sequences. They have different methods of calculating their characteristics, so first I need to find out what kind of sequence you have.

An arithmetic sequence has a common difference between terms. 48-51 = 45-48, so this could certainly be an arithmetic sequence.

A geometric sequence has a common ratio between terms. 48/51 ≠ 45/48, so this is not a geometric sequence.

So it is arithmetic.

Let a = the first term in an arithmetic sequence and let d = the common difference between terms (that is, the second term is a + d, the third term is a + 2d, etc.)

Then a + dn is the value of the (n+1)^th term.

I'll show you how to use this idea in my sequence: 8, 13, 18, ..., 88.

You can see that a = 8 and d = 5. I want to know what term has the value 88.

So I use the idea above a + dn = (n+1)^th term and I substitute in the values I know:

8 + 5n = 88

Now I solve for n:

8 + 5n - 8 = 88 - 8
5n = 80
5n ÷ 5 = 80 ÷ 5

n = 16.

Since this is the (n+1)^th term, this is the 17^th term in the sequence.

Now you try it the same way with your sequence.

Hope this helps
Stephen La Rocque.

Jesse,

Each successive term is obtained by adding -3 to the previous term so you need to find out how many -3's get you from 51 to -75. Try it with 48 then 45 then 42 to get yourself going.

Penny