anonymous
  • anonymous
ANY HELP IS APPRECIATED!!!! :) If the coefficient of the second term of (2a+b)^n is 80, what is the coefficient of the fourth term??
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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dumbcow
  • dumbcow
hmm well 2nd term would be: \[n(2a)^{n-1}b = 80\] 4th term is \[\frac{n!}{(n-3)! 3!} (2a)^{n-3} b^{3}\] not sure where to go since there are 3 unknowns and no more given information ?
dumbcow
  • dumbcow
oh oops i was looking at whole term not just coefficient... coefficient of 2nd term is \[n2^{n-1} = 80\] solve for n \[2^{n} = \frac{160}{n}\] \[n=5\] 4th term coefficient is \[nC3* 2^{n-3}\] \[= 5C3 * 2^{2}\] \[= 40\]
anonymous
  • anonymous
^ OMG words cannot describe how thankful I am to you for solving this!! :):):) Thank you sooo much! This was on my final today and I guessed 40 out of pure coincidence

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dumbcow
  • dumbcow
haha your welcome ... glad you got lucky :) figuring out n=5 is the tricky part of this whole thing

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