Question

Johann borrows money from his parents to purchase a bike. He makes weekly payments to his parents to repay the money borrowed. The total amount of money repaid at the end of week n can be represented using the recursive formula mc008-1.jpg. At the end of the fourth week, Johann had repaid his parents a total of $55. What is the total amount Johann had repaid his parents at the end of the first week?
$10
$20
$25
$35

Answer 1

I can’t see the image you attached. Could you type the recursive formula here (for example "T_n = T_{n-1} + 5n" or "T_n = 2T_{n-1} + 3")?

If you prefer, here is how to get the first-week total once you give the recursion:
- If T_n = T_{n-1} + f(n), then T_1 = T_4 − [f(2)+f(3)+f(4)].
- If T_n = r·T_{n-1}, then T_1 = T_4 / r^3.
- If T_n = a·T_{n-1} + b, expand to express T_4 in terms of T_1 and solve for T_1.

Send the exact formula and I’ll compute which choice (10, 20, 25, or 35) is correct.