Question

Your friend asks you to help him with his dog grooming business and will pay you 4 4 pennies for the first job. You agree to help if he quadruples your payment for each job completed. After 2 2 grooming jobs, you will receive 16 16 pennies, and after 3 3 grooming jobs, you will receive 64 64 pennies. Complete and solve the equation that finds the number of pennies he will pay you after the 9th 9th dog grooming job.

Answer 1

Answer:

You will receive 262,144 pennies after completing the 9th job.

Step-by-step explanation:

Given:

Payment for 1st job = 4 pennies

The payment is quadrupled after this for each job completed.

Payment after 2 jobs = 16 pennies

Payments after 3 jobs = 64 pennies

To find the number of pennies you will receive after the 9th job.

Solution:

Let $a_1$ represent the payment after 1st job.

$a_1=4$

$a_2=16$

$a_3=64$

The sequence is in geometric sequence with common ratio = 4

The n$th$ term of a geometric sequence is given as:

$T_n=a_1r^{(n-1)}$

For the sequence:

$a_1=4$

$n=9$

$r=4$

For the sequence we need the payment after 9th job. So, we are finding $T_9$.

$T_9=4(4)^{(9-1)}$

$T_9=4(4)^{8}$

$T_9=4(65536)$

$T_9=262144$

Thus, you will receive 262,144 pennies after completing the 9th job.