Respuesta :
each term after the first is 4 times the previous one, so second term is
-6*4 = -24
first 6 terms are -6,-24, -96, -384, -1536, -6144
-6*4 = -24
first 6 terms are -6,-24, -96, -384, -1536, -6144
Answer:
The first six terms of the sequence are -6, -24, -96, -384, -1536 and -6144.
Step-by-step explanation:
Given information : [tex]a_1=-6,a_n=4\cdot a_{n-1}[/tex].
It means the first term of the sequence is -6 and recursive formula is
[tex]a_n=4\cdot a_{n-1}[/tex]
Substitute n=2, to find the second term.
[tex]a_2=4\cdot a_{2-1}=4\cdot a_{1}=4\cdot (-6)=-24[/tex]
Substitute n=3, to find the third term.
[tex]a_3=4\cdot a_{3-1}=4\cdot a_{2}=4\cdot (-24)=-96[/tex]
Substitute n=4, to find the 4th term.
[tex]a_4=4\cdot a_{4-1}=4\cdot a_{3}=4\cdot (-96)=-384[/tex]
Substitute n=5, to find the 5th term.
[tex]a_5=4\cdot a_{5-1}=4\cdot a_{4}=4\cdot (-384)=-1536[/tex]
Substitute n=6, to find the 6th term.
[tex]a_6=4\cdot a_{6-1}=4\cdot a_{5}=4\cdot (-1536)=-6144[/tex]
Therefore the first six terms of the sequence are -6, -24, -96, -384, -1536 and -6144.
