Question

Mr. Morris asked Rob to shovel the snow from his driveway every day that it snowed during the month of January. He agreed to pay Rob $0.01 for the first day, $0.02 for the second day, $0.04 for the third day, $0.08 for the fourth day, and so on. If it snowed for 13 days in January, how much would Mr. Morris pay Rob on the 13th day?

Do not answer if you do not know. Only good answers with explanations.

Answer 1

Total amount to be paid on 13th day is $40.96.

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
`n^(th)` term of a GP is given by:

`a_(n) =ar^(n-1)`

Where, a is the first term of GP

r is the common ratio

We have to find the
`13^(th)` term of the GP as per question statement.

Putting the values in the formula above:

n = 13

a = 0.01 and

r = 2

`a_(13) = 0.01 * 2^(13-1)\\\Rightarrow 0.01 * 2^(12) \\\Rightarrow 0.01 * 4096\\\Rightarrow 40.96`

Total amount to be paid on 13th day is $40.96.