Question

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??

Answer 1

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 ?

Answer 2

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
\[nC3* 2^{n-3}\]
\[= 5C3 * 2^{2}\]
\[= 40\]

Answer 3

^ 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

Answer 4

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