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1.6 Sequences and Series

1.6 Sequences and Series

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Question 142

A design engineer models the attenuation of a high-frequency signal as it passes through a sequence of 7 capacitive filters. The intensity I I\,I relative to the source is given by I=(1−15x)7\displaystyle I = (1 - \frac{1}{5}x)^7I=(1−51​x)7, where x x\,x is a tuning parameter.

a.

Determine the first four terms, in ascending powers of xxx, of the binomial expansion of

(1−15x)7 \left(1 - \frac{1}{5}x\right)^7 (1−51​x)7

giving each term in its simplest form.

[4]
b.

In a modified circuit, the output signal is scaled such that the final intensity is represented by the expansion of

(15x+2)(1−15x)7 (15x + 2)\left(1 - \frac{1}{5}x\right)^7 (15x+2)(1−51​x)7

Find the coefficient of x3 x^3\,x3 in this new expansion, giving your answer as a fraction in simplest form.

[3]
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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