Answer:
The first 6 terms are -7,-14,-28,-56,-112,-224
Step-by-step explanation:
The given sequence is defined recursively by:
[tex]a_1=-7[/tex] and [tex]a_n=2(a_{n-1})[/tex]
When n=2
[tex]a_2=2(a_{2-1})[/tex]
[tex]a_2=2(a_{1})[/tex]
[tex]a_2=2(-7)=-14[/tex]
When n=3
[tex]a_3=2(a_{3-1})[/tex]
[tex]a_3=2(a_{2})[/tex]
[tex]a_3=2(-14)=-28[/tex]
When n=4
[tex]a_4=2(a_{4-1})[/tex]
[tex]a_4=2(a_{3})[/tex]
[tex]a_4=2(-28)=-56[/tex]
When n=5
[tex]a_5=2(a_{5-1})[/tex]
[tex]a_5=2(a_{4})[/tex]
[tex]a_5=2(-56)=-112[/tex]
When n=6
[tex]a_6=2(a_{6-1})[/tex]
[tex]a_6=2(a_{5})[/tex]
[tex]a_6=2(-112)=-224[/tex]
The first 6 terms are -7,-14,-28,-56,-112,-224