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.
number of nickels for 8th bracelet =
Payment for the 8th bracelet = nickels
To find the number of nickels your friend will pay you for the 8th bracelet, we first need to identify the pattern in payment for each bracelet.
You are given that:
– For the 1st bracelet: 6 nickels
– For the 2nd bracelet: 6 nickels × 6 = 36 nickels
– For the 3rd bracelet: 36 nickels × 6 = 216 nickels
From this, we can see that the payment for each bracelet is multiplied by 6 compared to the previous one.
This can be modeled as a geometric sequence where:
– Payment for the 1st bracelet (P1) = 6
– Payment for the 2nd bracelet (P2) = 6 × 6 = 36
– Payment for the 3rd bracelet (P3) = 36 × 6 = 216
So, we can generalize the payment formula:
– Payment for the nth bracelet = 6 × (6^{(n-1)})
Now, let’s calculate the payment for the 8th bracelet (n = 8):
– Payment for the 8th bracelet = 6 × (6^{(8-1)}) = 6 × (6^{7})
Next, we calculate (6^{7}):
– (6^{7} = 279936)
Now, multiply by 6:
– Payment for