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1.4 Sequences and Series

1.4 Sequences and Series

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Question 219

The first three terms, in ascending powers of xxx, of the binomial expansion of (16+5x)12(16 + 5x)^{\frac{1}{2}}(16+5x)21​ are given by

(16+5x)12≈a+58x−25512x2 (16 + 5x)^{\frac{1}{2}} \approx a + \frac{5}{8}x - \frac{25}{512}x^2 (16+5x)21​≈a+85​x−51225​x2

where aaa is a constant.

a.

State the range of values of xxx for which this expansion is valid.

Choose from the options below:

∣x∣<516∣x∣<165∣x∣<4∣x∣<1 |x| < \frac{5}{16} \quad |x| < \frac{16}{5} \quad |x| < 4 \quad |x| < 1 ∣x∣<165​∣x∣<516​∣x∣<4∣x∣<1
[2]
b.

Find the value of aaa.

Choose from the options below:

14816 1 \quad 4 \quad 8 \quad 16 14816
[2]
Markscheme

1.4 Sequences and Series Questions

  1. A Level
  2. /Maths
  3. /1.4 Sequences and Series

308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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