Question

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?

Answer 1

The correct answer is $25

Answer 2

Answer: $ 25

Explanation:

Given: The amount of money repaid can be represented using the recursive formula
`a_n=50+a_(n-1)`, where n is the number of week.

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

Thus,
`a_4=50+a_3`

`\Rightarrow175=50+a_3\\\Rightarrow\ a_3=175-50=125`

Now,
`a_3=50+a_2`

`\Rightarrow125=50+a_2\\\Rightarrow\ a_2=125-50=75`

`a_2=50+a_1`

`\Rightarrow75=50+a_1\\\Rightarrow\ a_1=75-50=25`

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