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| Math Central | Quandaries & Queries |
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Question from Vickie, a parent: Hello, Here's the question. Ryan wanted to play basketball on a team, He started practicing shooting everyday to improve his skills. The first day he make 5 shots, the second day he made 12 shots, the third day he made 19 shots, and the fourth day he made 26 shots. If the first day was March 1 and the pattern continues, how many shots will Ryan make on the last day of April and the last day of July? My daughter's answers were 425 for April and 1069 for July. Are these correct and what would be the formula for this question? ? +N=? I don't know please help. Thank you, |
We have two responses for you
Vickie,
I agree with your daughter's answers. Ryan starts with 5 shots and each day thereafter he makes 7 more shots than the day before.
Day 1: 5 shots
Day 2: 5 + 1 × 7 shots
Day 3: 5 + 2 × 7 shots
Day 4: 5 + 3 × 7 shots
Day 5: 5 + 4 × 7 shots
Do you see the pattern? The number of sevens added is one less than the day number. How many shots does he make on day n?
Penny
Vickie,
The first day he made 5 shots,
the second day he made 12 shots,
the third day he made 19 shots,
and the fourth day he made 26 shots.
(1) How is each of these numbers related to the one before it?
(2) How are the second, third, fourth related to the first? How would the tenth be related to the first? The hundredth? The n'th?
(3) You should now be able to say what the n'th number is.
Good Hunting!
-RD
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