The scenario as a sequence recursively and explicitly is
[tex]a_{1}[/tex] = 9,000 ; [tex]a_{n}[/tex] = 0.86 • [tex]a_{n-1}[/tex]
[tex]a_{n}=9,000(0.86)^{n-1}[/tex]
Step-by-step explanation:
The recursive formula for the nth term of a geometric sequence is
[tex]a_{1}[/tex] = first term ; [tex]a_{n}[/tex] = r • [tex]a_{n-1}[/tex] , where
The explicit formula for the nth term of a geometric sequence is
[tex]a_{n}=a(r)^{n-1}[/tex] , where
∵ A scooter (small motorcycle) is bought at a price of $9,000
∵ It loses 14% of its value very year
- That means the new price of it will be 100% - 14% of the
previous year
∵ 100% - 14% = 86%
∵ 86% = 86 ÷ 100 = 0.86
∴ Each year the price will be 0.86 of the price of the previous year
∴ The common ratio r = 0.86
∵ The initial price of the scooter is $9,000
∴ [tex]a_{1}[/tex] = 9,000
∵ r = 0.86
- Substitute them in the the recursive formula
∴ [tex]a_{1}[/tex] = 9,000 ; [tex]a_{n}[/tex] = 0.86 • [tex]a_{n-1}[/tex]
∵ a = 9,000
∵ r = 0.86
- Substitute them in the the explicit formula
∴ [tex]a_{n}=9,000(0.86)^{n-1}[/tex]
The scenario as a sequence recursively and explicitly is
[tex]a_{1}[/tex] = 9,000 ; [tex]a_{n}[/tex] = 0.86 • [tex]a_{n-1}[/tex]
[tex]a_{n}=9,000(0.86)^{n-1}[/tex]
Learn more:
You can learn more about the sequences in brainly.com/question/1522572
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