SOLUTION: Find the seventh term of (x+3)^9

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Question 1033553: Find the seventh term of (x+3)^9
Found 3 solutions by stanbon, ikleyn, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
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Find the seventh term of (x+3)^9
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The coefficients of that expansion are::
9C9, 9C8, 9C7,...9C3,9C2,9C1,9C0
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Ans: (9C3)x^3*3^6 = 84x^3*729 = 61236x^3
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Cheers,
Stan H.
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Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the seventh term of (x+3)^9
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It is C%5B9%5D%5E6%2Ax%5E3%2A3%5E6 = 84%2Ax%5E3%2A3%5E6 = 61236%2Ax%5E3,

where C%5B9%5D%5E6 = %289%2A8%2A7%2A6%2A5%2A4%29%2F%281%2A2%2A3%2A4%2A5%2A6%29 = 3%2A4%2A7 = 84

is the corresponding coefficient of the binomial expansion, equal to the number of combinations of 9 things taken 6 at a time.

On the binomial expansion read this lesson  Binomial Theorem, Binomial Formula, Binomial Coefficients and Binomial Expansion.

On the combinations read this lesson  Introduction to Combinations. 

One more useful link is this lesson  The Pascal's triangle in this site.

Answer. The seventh term of  %28x%2B3%29%5E9  is  61236%2Ax%5E3.


Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Find the seventh term of (x+3)^9
The good lady above made an error.

Rule:
The (r+1)st term of %28A%2BB%29%5En is nCr%2AA%5E%28n-r%29%2AB%5Er

n = 9

r+1 = 7
  r = 6

Substitute A=x, B=3, n=9, r=6 in the above rule  

The (6+1)st term of %28x%2B3%29%5E9 is 9C6%2Ax%5E%289-6%29%2A3%5E6

The 7th term of %28x%2B3%29%5E9 is 84%2Ax%5E3%2A729

The 7th term of %28x%2B3%29%5E9 is 61236x%5E3

Edwin