Question

Tickets sales for the bake sale were underway. Four people bought tickets on the first day of sales. Twice as much people bought tickets on the second day,and each day after that,twice as many people bought tickets. How many were sold after 16 days? 20 days?

Answer 1

`a_(16) = 65536`

`a_(20) = 1048576`

Explanation:

On the first day the number of people who bought the tickets is 4.

This represents the first term of a sequence.

`a_1=4`

Twice as much people bought tickets on the second day,and each day after that,twice as many people bought tickets.

This means the sequence is geometric with common ratio:

`r = 2`

The expresion for the 16th day is:

`a_(16) = a_(1) {2}^(15)`

`a_(16) = 2 * {2}^(15)`

`a_(16) = 65536`

The expresion for the 20th day is

`a_(20) = a_(1) {2}^(19)`

`a_(20) =2 * {2}^(19)`

`a_(20) = 1048576`