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1.7 D: Sequences and series

1.7 D: Sequences and series

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Question 184

In a digital signal processing loop, the gain factors GnG_nGn​ follow a recurrence relation defined by:

G1=0.8andGn+1=2Gn,n≥1 G_1 = 0.8 \quad \text{and} \quad G_{n+1} = \frac{2}{G_n}, \quad n \ge 1 G1​=0.8andGn+1​=Gn​2​,n≥1
a.

Calculate the values of G2G_2G2​, G3G_3G3​, and G4G_4G4​.

[3]
b.

Identify the period of this sequence.

[1]
c.

Evaluate the sum of the first 61 gain factors, ∑n=161Gn\sum_{n=1}^{61} G_n∑n=161​Gn​.

[3]
Markscheme

1.7 D: Sequences and series Questions

  1. A Level
  2. /Maths
  3. /1.7 D: Sequences and series

308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 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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