Posted by Gemini on Monday, October 19, 2009 at 2:10pm.
the Q is :
Given that (1+ax)^n = 1 + 30x +375x^2+.... find the values of the constants a and n .
I know that :
(i am writing (n 1) as the coefficient of n)
(n 1) *ax = 30x
(n 2) *(ax)^2 = 375x^2
which can be written as
(n 1)* a = 30
(n 2)*a^2 = 375
I solved this only by intuition and got n = 6 and a = 5
but does anyone know how to calculate it otherwise?
math (binomial exp) - bobpursley, Monday, October 19, 2009 at 3:02pm
Remember Pascal's triangle?
your coefficents are 1,30,375
So, your a=6, then n=6 (last row) and verify by a^2*15=375 yes, you are correct.
math (binomial exp) - Reiny, Monday, October 19, 2009 at 5:21pm
The first 3 terms of (1 + ax)^n
= 1 + n(ax) + n(n-1)/2(a^2x^2) + ...
so nax = 30x
na = 30
a = 30/n
n(n-1)/2(a^2x^2) = 375x^2
n(n-1)(900/n^2) = 750
900(n-1) - 750n
n = 5
then a = 30/5 = 6
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