MATH SOLVE

2 months ago

Q:
# 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.

Accepted Solution

A:

Answer:The first five terms are;-3,-7,11,-29,69Step-by-step explanation:The recursive definition of the sequence is [tex]a_1=-3,[/tex], [tex]a_2=-7[/tex] and [tex]a_n=a_{n-2}-2a_{n-1}[/tex].When n=3, we obtain;[tex]a_3=a_{3-2}-2a_{3-1}[/tex].[tex]\implies a_3=a_{1}-2a_{2}[/tex].[tex]\implies a_3=-3-2(-7)[/tex].[tex]\implies a_3=11[/tex].When n=4 [tex]\implies a_4=a_{2}-2a_{3}[/tex].[tex]\implies a_4=-7-2(11)=-29[/tex].When n=5[tex]\implies a_5=a_{3}-2a_{4}[/tex].[tex]\implies a_4=11-2(-29)=69[/tex].Therefore the first five terms are;-3,-7,11,-29,69