In a digital signal processing loop, the gain factors GnG_nGn follow a recurrence relation defined by:
G1=0.8andGn+1=2Gn,n≥1G_1 = 0.8 \quad \text{and} \quad G_{n+1} = \frac{2}{G_n}, \quad n \ge 1G1=0.8andGn+1=Gn2,n≥1
Calculate the values of G2G_2G2, G3G_3G3, and G4G_4G4.
Identify the period of this sequence.
Evaluate the sum of the first 61 gain factors, ∑n=161Gn\sum_{n=1}^{61} G_n∑n=161Gn.
Practise Edexcel A Level Maths 3.7 Recurrence Relations with exam-style questions for A Level Maths. 36 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.