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?

1

11

121 n=2

1331

14641 n=4

1,5,10,10,5,1

1,6,15,20,15,6,1 n=6

your coefficents are 1,30,375

a*something=30

a^2*next coefficent=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
Or

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

and

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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