Preview Activity

1.

Consider the recurrence relation

a_{n} = 5 a_{n - 1} - 6 a_{n - 2} .

🔗

Since the

n

th term is given as a combination of the two previous terms, we will need two initial terms to determine the sequence. Different initial terms will give different sequences.

🔗

(a)

What sequence do you get if the initial conditions are

a_{0} = 1,

a_{1} = 2 ?

Give the first five terms (including 1 and 2).

🔗

(b)

Based on the first few terms, what is a closed formula for this sequence?

🔗

a_{n} =

🔗

(c)

What sequence do you get if the initial conditions are

a_{0} = 1,

a_{1} = 3 ?

Give the first five terms.

🔗

(d)

Based on the first few terms, what is a closed formula for this sequence?

🔗

a_{n} =

🔗

(e)

What sequence do you get if the initial conditions are

a_{0} = 2,

a_{1} = 5 ?

Give the first five terms.

🔗

(f)

Based on the first few terms, what is a closed formula for this sequence?

🔗

a_{n} =

🔗

Hint.

How do the terms in this sequence relate to the terms in the previous two sequences?

🔗

Discrete Mathematics An Open Introduction, 4th Edition

Worksheet Preview Activity
A4 US

1.

(a)

(b)

(c)

(d)

(e)

(f)

Worksheet Preview Activity A4US

1.

(a)

(b)

(c)

(d)

(e)

(f)

Worksheet Preview Activity
A4 US