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.
308 exam-style questions on OCR (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.