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3.4 Sequences and Series (A-level only)

3.4 Sequences and Series (A-level only)

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Question 146

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

3.4 Sequences and Series (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.4 Sequences and Series (A-level only)

231 exam-style questions on WJEC A Level Maths 3.4 Sequences and Series (A-level only), covering 3.4.1 Sequences and Series (A-level only), 3.4.2 Sequences and Series (A-level only), 3.4.3 Sequences and Series (A-level only), 3.4.4 Sequences and Series (A-level only), 3.4.5 Sequences and Series (A-level only), 3.4.6 Sequences and Series (A-level only), and 3.4.7 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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