what is the third term in the expansion of $\displaystyle (a-3b)^4$
Also the middle term of the expansion $\displaystyle ($sinx$\displaystyle +2)^4$
Well then I assume it is a Maclaurin series you want
$\displaystyle x\sin(2x)=\sum_{n=0}^{\infty}\frac{(-1)^n(2x)^{2n+2}}{(2n+1)!}$
So what you want is this
$\displaystyle \sum_{n=0}^{3}\frac{(-1)^n(2x)^{2n+2}}{(2n+1)!}$
But there will be no 7 term, a 6 and 8 term though
P.S. This is hardly an Algebra/Pre-algebra question.