Question

On Thanksgiving Thursday, Tom ate some green beans. The next day he couldn't stop thinking about how good the green beans were and ate seven more green beans than he had eaten on Thursday. Each day after that he ate seven more green beans than the day before. By the following Wednesday night he had eaten a total of 161 green beans for the whole week.

Answer 1

2 green beans

Explanation:

Let the number of beans Tom ate on thursday be
`a`.

Let
`d` be the difference between the number of beans he eats on a day and its previous day.

It is given that he eats 7 more beans every day than the previous day.

So,
`d=7`

So the number of beans he eats is
`a,a+x,a+2* x,a+3* x ,...`

This is a arithmetic progression because the difference between any two terms in the series is constant.

There are seven days between thursday and following wednesday both inclusive.

Let
`n` be the number of terms in arithmetic progression.

Sum of first n terms in arithmetic progression is
`(2* a +(n-1)* d)(n)/(2)`

Since it is given that he ate 161 in total.

`(2* a +(n-1)* d)(n)/(2)`
`= 161`

substituting
`n=7` and
`d=7`,

`(2* a +(7-1)* 7)(7)/(2)=161\\ 2* a+42=46\\2* a=4\\a=2`

So,he ate 2 beans on thursday.