The expansion for a binomial is - $(a+b)^n=\sum_{k=0}^n{n\choose k}a^{n-k}b^{k} $
But it could also be this $(a+b)^n=\sum_{k=0}^n{n\choose k}a^kb^{n-k}$
Both of the expansions are correct because the pascal's triangle is palindromic, meaning that it doesn't matter whether we write the terms from the left end or from the right end. The first expression, which has $a^{n-k}$ is written from the left end, while the other one is written from the right end. The problem arises when I try to find the nth term in an arbitrary expansion $(a+b)^n$. For the first formula it comes out to be $T(r+1) = C(n,r) a^{n-r}b^r$
While in the second expansion the exponent of $a$ will be $k$, not $(n-k)$. Now, in class, I was presented with a question to find the 5th term of some expansion. I used the second formula and returned with an incorrect answer, the correct one having come from the first formula. I tried asking my teacher, but I couldn't get a satisfactory response. Aren't such questions ambiguous? Shouldn't it be provided in the question whether we take the powers of $a$ in ascending or descending order? Or, if one term is negative, it would suffice to say whether the first term is positive or negative (if the index is odd). Should I just accept the first expression as convention? Any insight would be greatly appreciated as this has been troubling me for a while now. Thanks!
P.S. An example of such a problem is 