Your Friend Asks You To Help Him With His Dog Grooming Business And Will Pay You 4 Pennies For The First Job. You Agree To Help If He Quadruples Your

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

The sequence by which he recieves wages is:

4, 16, 64,.....

Its is in GP with First term(a) = 4 and common ratio(r) = 16/4 = 4.

n-th term of a GP, a_{n}=ar^{n-1}

So, equation for finding wages he will recieve at n-th day:

a_{n}=4\times4^{n-1}

a_{n}=4^{1+n-1}=4^{n}

Wage at 9-th day.

a_{9}=4^{9}=262144 pennies


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