Respuesta :

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

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