Question

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

Answer 1

-13,8,-5,3,-2,1

Explanation:

right on edg 2023

Answer 2

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

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