Find a, band n in the expansion of (a+ b)nif the first three terms of the expansion are 729, 7290 - Maths - Binomial Theorem

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

Gopal Mohanty · Accepted Answer

It is known that (r + 1)th term, (Tr+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

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.