Find the first six terms of the sequence described by the following recursive formula: an = an - 1 + an - 2 where a3 = - 5 and a4 = 3

Now we have: - 13, 8, - 5, 3, - 2, 1

Step-by-step explanation:

This is a Fibonacci sequence.

though modified.

so a_n = a_ (n-1) + a_ (n-2)

with a_3 = - 5,

a_4 = 3

a_3 = - 5 = a_2 + a_1

a_4 = 3 = a_3 + a_2 = - 5 + a_2

then a_2 = 3 + 5 = 8

then.

a_3 = - 5 = a_2 + a_1 = 8 + a_1

a_1 = - 5 - 8 = - 13

We now have: - 13, 8, - 5, 3, ...

Now we can find a_5 and a_6

a_5 = a_4 + a_3 = 3 + - 5 = - 2

a_6 = a_5 + a_4 = - 2 + 3 = 1

Now we have: - 13, 8, - 5, 3, - 2, 1