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

Algebra ->  Sequences-and-series -> 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      Log On


   

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) About Me  (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 t%5Bn%5D=%284%2F3%29n-6


Let's find the first term:

t%5Bn%5D=%284%2F3%29n-6 Start with the given sequence


t%5B0%5D=%284%2F3%29%280%29-6 Plug in n=0 (a good number to start with). Note: you can start with any value of "n"


t%5B0%5D=0-6 Multiply


t%5B0%5D=-6 Subtract


So the first term is t%5B0%5D=-6


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Now let's find the second term:

t%5Bn%5D=%284%2F3%29n-6 Start with the given sequence


t%5B1%5D=%284%2F3%29%281%29-6 Plug in n=1 (the next term after t%5B0%5D)


t%5B1%5D=4%2F3-6 Multiply


t%5B1%5D=4%2F3-18%2F3 Multiply 6 by 3%2F3


t%5B1%5D=%284-18%29%2F3 Combine the fractions.


t%5B1%5D=-14%2F3 Subtract


So the second term is t%5B1%5D=-14%2F3


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


Now take the difference of those two terms


d=t%5B1%5D-t%5B0%5D=-14%2F3-%28-6%29=-14%2F3%2B6=-14%2F3%2B18%2F3=%28-14%2B18%29%2F3=4%2F3


So the common difference is d=4%2F3 which means that the answer is B)


Notice how the coefficient the term "n" is also 4%2F3. 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 4%2F3 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.