Problem No. 25. Reading skills

Reading is the way to improve your reading skills!

To improve his reading skills, Scott reads a half and a sentence more from what he read the day before. How many sentences he has read in 7 days, if he read 30 sentences on the first day?

Student tip

Solve partially i.e. find how many sentences he read each day.

Solution

We will solve the problem "day by day". The number of sentences that Scott reads each of the days is:
1st day: $30,$
2nd day: $30 + \frac{1}{2} \cdot 30 + 1 = 30 + 15 + 1 = 46,$
3th day: $46 + \frac{1}{2} \cdot 46 + 1 = 46 + 23 + 1 = 70,$
4th day: $70 + \frac{1}{2} \cdot 40 + 1 = 70 + 35 + 1 = 106,$
5th day: $106 + \frac{1}{2} \cdot 106 + 1 = 106 + 53 + 1 = 160,$
6th day: $160 + \frac{1}{2} \cdot 160 + 1 = 160 + 80 + 1 = 241,$
7th day: $241 + \frac{1}{2} \cdot 241 + 1 = 241 + 120,5 + 1 = 362,5,$
So, the total number of sentences that Scott has read is:
$30 + 46 + 70 + 106 + 160 + 241 + 362,5 = 1015,5$ sentences.