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

Answer:

(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.

Step-by-step 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:

$S_{n}=\frac{n}{2}\cdot [2a+(n-1)d]$

Compute the sum as follows:

$S_{n}=\frac{n}{2}\cdot [2a+(n-1)d]$

    $=\frac{43}{2}\cdot [2\cdot 17+(43-1)\cdot 2]\\\\=43\cdot [17+42]\\\\=2537$

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