Answer :

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)

a^{n} = 729

⇒ a^{6} = 729

⇒ a^{6} = (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.

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