Question

On Thanksgiving Thursday Carissa ate some

Answer 1

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:

$S_n=\frac{n}{2}(2a+(n-1)d)$

$S_7=\frac{7}{2}(2*x+(7-1)*7)$

$161=\frac{7}{2}(2x+6*7)$

$161=\frac{7}{2}(2x+42)$

$161*2=7(2x+42)$

$322=14x+294$

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

$t_n=a+(n-1)*d$

$499=2+(n-1)*7$

$499=2+7n-7$

$499=7n-5$

$499+5=7n$

$504=7n$

72=n

Hence final answer is 72nd day.