In the expansion of (1+px)^n in ascending powers of x, the second term is 18x and the third term is 135x^2.Find the values of n and p?

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Answer 1 · 2018-05-07T12:17:38

The answer is #{n=6 ; p=3}#

The binomial expansion is

#(1+px)^n=1+npx+((n)(n-1))/(2!)p^2x^2+.....#

The second term is

#npx=18x#, #=>#, #np=18#

The third term is

#((n)(n-1))/(2!)p^2x^2=135x^2#

#<=>#, #(n^2-n)p^2=2*135=270#

#=>#, #n^2p^2-np^2=270#

#np^2=n^2p^2-270=18^2-270=54#

#p=54/(np)=54/18=3#

#n=18/p=18/3=6#

Therefore,

#(1+3x)^6=1+18x+135x^2+...#