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.
326 exam-style questions on Edexcel A Level Maths Sequences and Series, 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. Each one has a worked solution and a mark scheme showing where the marks go.