Solve the linear recurrence relation

I’m working on a Mathematics exercise and need support.

Q1 Show ALL your WORK.

Solve the linear recurrence relation

LaTeX: a_n=7a_{n-1}-12a_{n-2}

a

n

=

7

a

n

1

12

a

n

2

,

with initial conditions LaTeX: a_0=1

a

0

=

1
and LaTeX: a_1=8.

Show ALL your WORK.

Q2 Solve the linear recurrence relation

LaTeX: a_n=8a_{n-1}-16a_{n-2}

a

n

=

8

a

n

1

16

a

n

2

with initial conditions LaTeX: a_0=3

a

0

=

3
and LaTeX: a_1=4.

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