Question

Michelle likes chocolate but it causes acne. She chooses to limit herself to three pieces of chocolate every week. Except the first week, when she eats ten pieces. How many pieces has she eaten after seven weeks?

Is this an arithmetic or geometric sequence? What is the general term? What is the 7th term?

Answer 1

She eats 10 her first week so she eats 3 pieces for the next six weeks (3 each week)
10 + 3(6) = 28
10+3+3+3+3+3+3=28
7th term is 28
Arithmetic sequence

Answer 2

Explanation:

Given that Michelle likes chocolate but it causes acne. She chooses to limit herself to three pieces of chocolate every week.

Except the first week, when she eats ten pieces.

This table below shows the chocolates totally she has eaten after each week upto 7 weeks
`I week = 10\\II week = 10+3 = 13\\III week=10+3+3 =16\\...Vii week = 10+3+3..+3 (6 times) =28`

Thus we find that this is a sequence which increases by a constant difference 3.

Hence this is an arithmetic sequence.

I term = 10 and common difference = 3

Hence nth term

`a_n=10+(n-1)3 =3n+7\\a_7 =10+(7-1)3 = 28`