Question

Jerry uses an exercise program to help him eventually do 100 push-ups. He started with 17 push-ups in Week 1 and planned to increase the number of push-ups by 2 each week. Show your work. a) In which week does Jerry expect to reach his goal? b) What is the total number of push-ups he will have done when he reaches his goal?

Answer 1

(a) Jerry expect to reach his goal by week 43rd.

(b) The total number of push-ups Jerry will have done when he reaches his goal is 2,537.

Explanation:

It is provided that Jerry wants to do 100 push-ups. He started with 17 push-ups in Week 1 and planned to increase the number of push-ups by 2 each week.

the number of push-ups done each week by Jerry follows a arithmetic progression with the first terms as, a = 17, common difference as, d = 2 and the last terms as, l = 100.

(a)

Compute the number of week it takes Jerry to reach his goal as follows:

The nth term of an AP is:

`t_(n)=a+(n-1)d`

Compute the value of n as follows:

`t_(n)=a+(n-1)d`

`100=17+(n-1)\cdot 2\\\\100-17=(n-1)\cdot 2\\\\83=2n-2\\\\2n=85\\\\n=42.5\\\\n\approx 43`

Thus, Jerry expect to reach his goal by week 43rd.

(b)

Compute the total number of push-ups he will have done when he reaches his goal as follows:

The sum of n terms of an AP is:

`S_(n)=(n)/(2)\cdot [2a+(n-1)d]`

Compute the sum as follows:

`S_(n)=(n)/(2)\cdot [2a+(n-1)d]`

`=(43)/(2)\cdot [2\cdot 17+(43-1)\cdot 2]\\\\=43\cdot [17+42]\\\\=2537`

Thus, the total number of push-ups Jerry will have done when he reaches his goal is 2,537.