SOLUTION: Which represents the common difference between successive terms in the sequence generated by tn=4/3n-6? Is it (a) -4/3 (b) 4/3 (c) -6 or (d)6 I know I am over thinking this quest

Question 177933: Which represents the common difference between successive terms in the sequence generated by tn=4/3n-6?
Is it (a) -4/3 (b) 4/3 (c) -6 or (d)6
I know I am over thinking this question :(
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The "common difference" is the difference between consecutive terms. So let's say we had the sequence: 1,2,3,4

The common difference is 1 since the difference between 1 and 2 is 1, the difference between 2 and 3 is 1, and the difference between 3 and 4 is 1.

So given any linear sequence, we can find the common difference by picking 2 terms and subtracting them. However, we need two terms from the sequence

Let's find the first term:

Start with the given sequence

Plug in (a good number to start with). Note: you can start with any value of "n"

Multiply

Subtract

So the first term is

------------------------------

Now let's find the second term:

Start with the given sequence

Plug in (the next term after )

Multiply

Multiply 6 by

Combine the fractions.

Subtract

So the second term is

==============================================

Now take the difference of those two terms

So the common difference is which means that the answer is B)

Notice how the coefficient the term "n" is also . This is no coincidence. It turns out that the coefficient in front of the term "n" is the common difference since you are adding multiples of to -6.

So after all of that, we could have just said that the common difference is just the value in front of the "n". So once you understand how to find the common difference (and what it means), then you can quickly find the common difference.

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