Question

Your friend asks you to make friendship bracelets and will give you 6 nickels for the first bracelet. You agree to help if she multiplies your payment by 6 for each bracelet completed. After 2 bracelets, you will receive 36 nickels, and after 3 bracelets, you will receive 216 nickels. Complete and solve the equation that finds the number of nickels she will pay you after making the 8th bracelet.

Answer 1

To find the number of nickels your friend will pay you after making the 8th bracelet, you need to determine the pattern in the amounts received so far and use it to calculate the 8th payment. The 8th payment will be 46,656 nickels.

Step-by-step explanation:

To find the number of nickels your friend will pay you after making the 8th bracelet, we need to determine the pattern in the amounts you have received so far. Let's start by listing the payments for the first few bracelets:

1st bracelet: 6 nickels

2nd bracelet: 36 nickels

3rd bracelet: 216 nickels

From these amounts, we can see that each subsequent payment is obtained by multiplying the previous payment by 6. So, the pattern is:
1st payment: 6
2nd payment: 6 x 6 = 36
3rd payment: 36 x 6 = 216

To find the 8th payment, we can use this pattern:

8th payment: 216 x 6 x 6 x 6

Simplifying the equation, we get:

8th payment: 6^3 x 6^3

= 6^(3+3)

= 6^6

= 46,656 nickels

Answer 2

for n=1, the result is 6

for n=2, the result is 36
so it is
an=6ⁿ

8th bracelet is 6⁸=1679616 nickles (about $83980.8)