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Johann borrows money from his parents to purchase a bike. He makes weekly payments to his parents to repay the money borrowed. The amount of money repaid can be represented using the recursive formula an=50+an-1. During the fourth week, Johann repaid his parents $175. How much total had Johann repaid after the first week, a1?

Respuesta :

The correct answer is $25
JeanaShupp

Answer: $ 25

Step-by-step explanation:

Given: The amount of money repaid can be represented using the recursive formula [tex]a_n=50+a_{n-1}[/tex], where n is the number of week.

Since during the fourth week, Johann repaid his parents $175.

Thus, [tex]a_4=50+a_3[/tex]

[tex]\Rightarrow175=50+a_3\\\Rightarrow\ a_3=175-50=125[/tex]

Now,  [tex]a_3=50+a_2[/tex]

[tex]\Rightarrow125=50+a_2\\\Rightarrow\ a_2=125-50=75[/tex]

[tex]a_2=50+a_1[/tex]

[tex]\Rightarrow75=50+a_1\\\Rightarrow\ a_1=75-50=25[/tex]

Hence, the total which Johann had repaid after the first week = $ 25

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