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
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.
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.
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