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1.6 Sequences and Series

1.6 Sequences and Series

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Question 149

A quantitative analyst models the projected value of a high-risk portfolio using the function V(x)=(4+kx)7V(x) = (4 + kx)^7V(x)=(4+kx)7, where xxx represents market volatility and kkk is a positive sensitivity constant.

a.

Find the first three terms, in ascending powers of xxx, in the expansion of

(4+kx)7 (4 + kx)^7 (4+kx)7

giving each term in its simplest form.

[3]
b.

Given that the coefficient of x2x^2x2 is exactly three-eighths of the coefficient of xxx, determine the value of kkk.

[2]
Markscheme

1.6 Sequences and Series Questions

  1. A Level
  2. /Maths
  3. /1.6 Sequences and Series

308 exam-style questions on OCR (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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