1.4.5 Sequences (A-level only)

In a digital signal processing loop, the gain factors $G_n$ follow a recurrence relation defined by:

G_1 = 0.8 \quad \text{and} \quad G_{n+1} = \frac{2}{G_n}, \quad n \ge 1

a.

Calculate the values of $G_2$ , $G_3$ , and $G_4$ .

[3]

b.

Identify the period of this sequence.

[1]

c.

Evaluate the sum of the first 61 gain factors, $∑n=161Gn\sum_{n=1}^{61} G_n$ .

[3]

In a digital signal processing loop, the gain factors $G_n$ follow a recurrence relation defined by:

G_1 = 0.8 \quad \text{and} \quad G_{n+1} = \frac{2}{G_n}, \quad n \ge 1

a.

Calculate the values of $G_2$ , $G_3$ , and $G_4$ .

[3]

b.

Identify the period of this sequence.

[1]

c.

Evaluate the sum of the first 61 gain factors, $∑n=161Gn\sum_{n=1}^{61} G_n$ .

[3]

1.4.5 Sequences (A-level only) Questions