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.
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:

Compute the value of n as follows:


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]](https://img.qammunity.org/2021/formulas/mathematics/high-school/9fgsl34x4k8szgrwh2jc0jochdi8mfid0r.png)
Compute the sum as follows:
![S_(n)=(n)/(2)\cdot [2a+(n-1)d]](https://img.qammunity.org/2021/formulas/mathematics/high-school/9fgsl34x4k8szgrwh2jc0jochdi8mfid0r.png)
![=(43)/(2)\cdot [2\cdot 17+(43-1)\cdot 2]\\\\=43\cdot [17+42]\\\\=2537](https://img.qammunity.org/2021/formulas/mathematics/high-school/x5fq40n0e4gs1ftq7w0bagkr19tgfxsqch.png)
Thus, the total number of push-ups Jerry will have done when he reaches his goal is 2,537.