Question

A scooter (small motorcycle) is bought at a price of $9,000. It loses 14% of its value very year. Express this scenario as a sequence recursively and explicitly (provide its general term).

Answer 1

The scenario as a sequence recursively and explicitly is

$a_{1}$ = 9,000 ;  $a_{n}$ = 0.86 • $a_{n-1}$

$a_{n}=9,000(0.86)^{n-1}$

Step-by-step explanation:

The recursive formula for the nth term of a geometric sequence is

$a_{1}$ = first term ;  $a_{n}$ = r • $a_{n-1}$ , where

• $a_{1}$ is the first term in the sequence
• r is the common ratio  between the consecutive terms

The explicit formula for the nth term of a geometric sequence is

$a_{n}=a(r)^{n-1}$ , where

• a is the first term
• r is the common ratio between the consecutive terms

∵ 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

∴ $a_{1}$ = 9,000

∵ r = 0.86

- Substitute them in the the recursive formula

∴ $a_{1}$ = 9,000 ;  $a_{n}$ = 0.86 • $a_{n-1}$

∵ a = 9,000

∵ r = 0.86

- Substitute them in the the explicit formula

∴ $a_{n}=9,000(0.86)^{n-1}$

The scenario as a sequence recursively and explicitly is

$a_{1}$ = 9,000 ;  $a_{n}$ = 0.86 • $a_{n-1}$

$a_{n}=9,000(0.86)^{n-1}$

Learn more:

You can learn more about the sequences in brainly.com/question/1522572

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