Find a , b and n in the expansion of ( a + b ) n if the first three terms of the expansion are 729, 7290 and 30375, respectively.
It is known that (r + 1)th term, (Tr+1), in the binomial expansion of (a + b)n is given by .
The first three terms of the expansion are given as 729, 7290, and 30375 respectively.
Therefore, we obtain
Dividing (2) by (1), we obtain
Dividing (3) by (2), we obtain
From (4) and (5), we obtain
Substituting n = 6 in equation (1), we obtain
a6 = 729
From (5), we obtain
Thus, a = 3, b = 5, and n = 6.