Answer:
Total amount to be paid on 13th day is $40.96.
Step-by-step explanation:
Mr. Morris pays Rob $0.01, $0.02, $0.04 ..... on 1st, 2nd , 3rd .... day respectively.
We can clearly see that the next number is becoming double of the previous value.
The above sequence of numbers are in a Geometric Progression with
First term, a = 0.01 and
Common ratio, r = 2
We have to find the total amount paid on 13th day.
We know that the [tex]n^{th}[/tex] term of a GP is given by:
[tex]a_{n} =ar^{n-1}[/tex]
Where, a is the first term of GP
r is the common ratio
We have to find the [tex]13^{th}[/tex] term of the GP as per question statement.
Putting the values in the formula above:
n = 13
a = 0.01 and
r = 2
[tex]a_{13} = 0.01 \times 2^{13-1}\\\Rightarrow 0.01 \times 2^{12} \\\Rightarrow 0.01 \times 4096\\\Rightarrow 40.96[/tex]
Total amount to be paid on 13th day is $40.96.
