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.

We know that-

So first 3 terms are

Also, it is given that their value are 729, 7290 and 30375

Therefore,

…(1)

…(2)

…(3)

Dividing (1) by (2)

…(4)

Dividing (2) by (3)

…(5)

Dividing (4) by (5)

⇒ 12(n-1) = 10n

⇒ 12n-12 = 10n

⇒ 2n = 12

⇒ n = 12/2

∴ n = 6

Putting n = 6 in (1)

aⁿ = 729

⇒ a⁶ = 729

⇒ a⁶ = (3)⁶

∴ a = 3

Putting a = 3, n = 6 in (5)

⇒ 6b = 30

⇒ b = 30/6

∴ b = 5

Thus, a = 3, b = 5 and n = 6.