Let number of cranberries did Carissa eat on Thanksgiving Thursday = x
Given that she ate 7 cranberries on each following day so that seems she is following arithmetic sequence.
Whose first term is a = x
common difference d = 7
Given that on following Wednesday night, she had eaten a
total of 161 cranberries for the whole week.
Wednesday means on 7th day from thanksgiving day.
Then sum of 7 terms of the sequence is 161
S7=161
Sum of arithmetic sequcen is given by formula:
[tex] S_n=\frac{n}{2}(2a+(n-1)d) [/tex]
[tex] S_7=\frac{7}{2}(2*x+(7-1)*7) [/tex]
[tex] 161=\frac{7}{2}(2x+6*7) [/tex]
[tex] 161=\frac{7}{2}(2x+42) [/tex]
[tex] 161*2=7(2x+42) [/tex]
[tex] 322=14x+294 [/tex]
322-294=14x
28=14x
2=x
Hence Carissa ate 2 cranberries on Thanksgiving Thursday.
Now we have to find the number of day on which Carissa will eat 499 cranberries.
So we will use nth term formula
[tex] t_n=a+(n-1)*d [/tex]
[tex] 499=2+(n-1)*7 [/tex]
[tex] 499=2+7n-7 [/tex]
[tex] 499=7n-5 [/tex]
[tex] 499+5=7n [/tex]
[tex] 504=7n [/tex]
72=n
Hence final answer is 72nd day.
