IB Maths AA SL AA 1.4 Binomial theorem and counting questions

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Question 1

Paper 1, no calculatorHard6 marks

For positive integers $n$ and $a$ consider the expansion of $(1+ax)^n$

The coefficient of $x^2$ is five times the coefficient of $x$ and the coefficient of $x^3$ is $\frac{8}{3}$ times the coefficient of $x^2$

(a)

Determine $n$ and $a$

[4]

(b)

Hence determine the sum of the coefficients of all even powers of $x$ including the constant term, in the expansion.

[2]

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