Let's assume that the number of pennies paid after cutting the 15th lawn is represented by P.
From the given information, we know that after the first lawn, you are paid 2 pennies. After the second lawn, you received double that amount, which is 4 pennies. After the third lawn, you received double that amount again, which is 8 pennies. This pattern continues, with the payment doubling each time.
Using this pattern, we can express the number of pennies paid after each lawn as a geometric sequence. The general term of a geometric sequence is given by the formula:
an = a * r^(n-1)
where:
an is the nth term
a is the first term
r is the common ratio
n is the number of terms
In this case, the first term (a) is 2 pennies, and the common ratio (r) is 2 because the payment doubles each time.
So, the equation to find the number of pennies paid after the nth lawn is:
P = 2 * 2^(n-1)
To find the number of pennies paid after the 15th lawn, we substitute n = 15 into the equation:
P = 2 * 2^(15-1)
P = 2 * 2^14
P = 2 * 16,384
P = 32,768 pennies
Your friend asks you to help cut grass this summer and will pay you 2 pennies for the first job. You agree to help if he doubles your payment for each job completed. After 2 lawns, you will receive 4 pennies, and after 3 lawns, you will receive 8 pennies.
Complete and solve the equation that finds the number of pennies he will pay you after cutting the 15th lawn.
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