When x=5/2, numerically the greatest term in the expansion of (3+2x)^15 is?

Thanks for asking this question.I hope my answer could clear your doubt.In a binomial expansion the greatest coefficient is of middle term and also for for a binomial having n power, number of terms in its expansion are (n+1).Therefore for (i)binomial having even n, middle term us Tn/2 +1 and for (ii) binomial having odd n middle term is either T(n-1)/2 +1 or T(n+1)/2 +1.Since in the given binomial power is 15 (odd).Therefore middle term will either be T7+1 or T8+1.T7+1 = 15C7(3)^8(2*5/2)^7 = 3.29*10^12T8+1 = 15C8(3)^7(2*5/2)^8 = 5.49 *10^12Hence, numerically greatest term is 9th term.** But there is a different formula for finding greatest term, I haven`t mentioned that here because of its complexity.