Q. 255.0( 6 Votes )
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 :
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.
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