Q. 13.5( 68 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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