The first four terms of the sequence are 3 , 6 , 12 , 24
Step-by-step explanation:
We need to find the first four terms of the sequence [tex]a_{n}=2a_{n-1}[/tex]
where [tex]a_{1}=3[/tex] to find them do that
∵ [tex]a_{n}=2a_{n-1}[/tex]
- Substitute n by 2 to find the 2nd term
∴ [tex]a_{2}=2a_{2-1}[/tex]
∴ [tex]a_{2}=2a_{1}[/tex]
∵ [tex]a_{1}=3[/tex]
∴ [tex]a_{2}=2(3)[/tex]
∴ [tex]a_{2}=6[/tex]
- Substitute n by 3 to find the 3rd term
∴ [tex]a_{3}=2a_{3-1}[/tex]
∴ [tex]a_{3}=2a_{2}[/tex]
∵ [tex]a_{2}=6[/tex]
∴ [tex]a_{3}=2(6)[/tex]
∴ [tex]a_{3}=12[/tex]
- Substitute n by 4 to find the 4th term
∴ [tex]a_{4}=2a_{4-1}[/tex]
∴ [tex]a_{4}=2a_{3}[/tex]
∵ [tex]a_{3}=12[/tex]
∴ [tex]a_{4}=2(12)[/tex]
∴ [tex]a_{4}=24[/tex]
The first four terms of the sequence are 3 , 6 , 12 , 24
Learn more:
You can learn more about the sequences in brainly.com/question/1522572
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