Question

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.

Answer 1

It is known that (r + 1)^th term, (T_r+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.