Question

Case Study Push-ups are a fast and effective exercise for building strength. These are helpful in almost all sports including athletics. While the push-up primarily targets the muscles of the chest, arms, and shoulders, support required from other muscles helps in toning up the whole body. Nitesh wants to participate in the push-up challenge. He can currently make 3000 push-ups in one hour. But he wants to achieve a target of 3900 push-ups in 1 hour for which he practices regularly. With each day of practice, he is able to make 5 more push-ups in one hour as compared to the previous day. If on first day of practice he makes 3000 push-ups and continues to practice regularly till his target is achieved. Keeping the above situation in mind answer the following questions:

1. Form an A.P representing the number of push-ups per day and hence find the minimum number of days he needs to practice before the day his goal is accomplished?
2. Find the total number of push-ups performed by Nitesh up to the day his goal is achieved.

Answer 1

i. 3000, 3005, 3010, ..., 3900.

a_n = a + (n − 1)d

3900 = 3000 + (n − 1)5

⇒ 900 = 5n − 5 ⇒ 5n = 905 ⇒ n = 181

Minimum number of days of practice = n − 1 = 180 days

ii. S_n = `n/2(a + l)`

= `181/2 xx (3000 + 3900)` = 624450 pushups