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1.7.1 Binomial expansion

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Question 77

The volume of a growing tropical fruit, V(x)V(x)V(x) in cm3\text{cm}^3cm3, after x x\,x weeks is modeled by the function

V(x)=(2+kx4)7 V(x) = \left(2 + \frac{kx}{4}\right)^7 V(x)=(2+4kx​)7

where k k\,k is a non-zero constant.

a.

Find the first 4 terms, in ascending powers of xxx, of the binomial expansion of V(x)V(x)V(x). Give each term in simplest form.

[4]
b.

Given that the coefficients of xxx, x2x^2x2, and x3 x^3\,x3 in this expansion form the first three terms of an arithmetic progression,

find, using algebra, the possible values of kkk.

[4]
Markscheme

1.7.1 Binomial expansion Questions

  1. A Level
  2. /Maths
  3. /1.7.1 Binomial expansion

144 exam-style questions on AQA A Level Maths 1.7.1 Binomial expansion. Each one has a worked solution and a mark scheme showing where the marks go.

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