The Question : 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:(i) 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(ii) Find the total number of push-ups performed by Nitesh up to the day his goal is achieved.
Solution for the question :
(i) 3000, 3005, 3010, …,3900. an = 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 day(ii) Sn = n/2 (a + l) Sn = 181/2 × (3000 + 3900) Sn = 624450 pushups
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