Question

Find the first five terms of the sequence given the following recursive formula:

a1 = -3, a2 = -7, and an = an-2 -2an-1 for n greater than or equal to 3.

Enter the terms separated by a comma.

Answer 1

Answer:

The first five terms are;

-3,-7,11,-29,69

Step-by-step explanation:

The recursive definition of the sequence is

$a_1=-3,$, $a_2=-7$ and $a_n=a_{n-2}-2a_{n-1}$.

When n=3, we obtain;

$a_3=a_{3-2}-2a_{3-1}$.

$\implies a_3=a_{1}-2a_{2}$.

$\implies a_3=-3-2(-7)$.

$\implies a_3=11$.

When n=4

$\implies a_4=a_{2}-2a_{3}$.

$\implies a_4=-7-2(11)=-29$.

When n=5

$\implies a_5=a_{3}-2a_{4}$.

$\implies a_4=11-2(-29)=69$.

Therefore the first five terms are;

-3,-7,11,-29,69