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=Gn2,n≥1Calculate 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 Sequences and Series with exam-style questions for A Level Maths. 156 questions covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series, 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.
