Given the following recurrence relation: An = (-2) An-1, with A0 = (-1)

determine the value of a5

Technically you could answer this one by one, by substituting n with 1, 2, 3, 4, then 5. Like here:

A1 = (-2) A1-1

= (-2) A0, then substituting A0 with - 1 ...

= (-2) (-1)

Which would mean A1=2. Then ...

A2 = (-2) A2-1

A2 = (-2) A1

A2 = (-2) (2)

Which would mean A2=-4.

By repeating this process you'd eventually get A4 ...

A5 = (-2) A4

if you did the steps right you'd get that A4 is - 16 ...

A5 = (-2) (-16).

Then simplify to get your answer.