## Cranberry Craving

On Thanksgiving Thursday, Carissa ate some cranberries. The next day she couldn’t stop thinking about how good the cranberries were and ate seven more cranberries than she had eaten on Thursday.

Each day after that she ate seven more cranberries than the day before. By the following Wednesday night she had eaten a total of 161 cranberries for the whole week.

62

Hi Emma,

Are you thinking about how many cranberries Carissa might have eaten? What does the 62 represent?

Thanks for thinking about our math story!

Max

I noticed that Carissa really must like cranberries. I also noticed that she would increase the number of cranberries she ate each day by 7. I was wondering what her starting number of cranberries was if less then a week later she had eaten 161.

I was wondering how many cranberries Carissa had at first. I think she had 2 to begin with.

I am wondering how many cranberries Carissa had at first. I think she ate 2 cranberries on Thanksgiving Thursday.

I am wondering if she ate 2 cranberries on Thanksgiving Thursday.

On Thanksgiving Carissa ate 2 cranberries, which the others have said. Here’s why:

Day 1: n;

Day 2: n + 7*1;

Day 3: n + 7*2;

Day 4: n + 7*3;

Day 5: n + 7*4;

Day 6: n + 7*5;

Day 7: n + 7*6;

If you add all of the multiples of 7 you get 147. The total, 161, minus 147 equals 14. That would be the “n”. Since there are 7 “n’s” you divide 14 by 7 and get 2.

This problem is an example of summing up an arithmetic sequence. The sum of an arithmetic sequence is n(a_0 + a_n)/2 where n is the number of terms in the sequence, and a_0 and a_n are the first and last terms respectively.

Since we don’t know how many she ate on Thanksgiving (the first day) let’s call that x. Since she ate 7 more than she did on the previous day after Thanksgiving, Carissa ate x +6*7 or x+42 the following Wednesday.

Therefore, 7*(x + x+42)/2 = 161 –> 7*(2x + 42)/2 = 161. Solving for x gives x = 2. Carissa started by eating 2 cranberries on Thanksgiving.