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Question
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
`sqrt3, sqrt6, sqrt9, sqrt12 ...`
Solution
`sqrt3, sqrt6, sqrt9, sqrt12`
Here,
a2 - a1 = `sqrt6 - sqrt3 = sqrt3 × 2 -sqrt3 = sqrt3(sqrt2 - 1)`
a3 - a2 = `sqrt9 - sqrt6 = 3 - sqrt6 = sqrt3(sqrt3 - sqrt2)`
a4 - a3 = `sqrt12 - sqrt9 = 2sqrt3 - sqrt3 × 3 = sqrt3(2 - sqrt3)`
⇒ an+1 - an is not the same every time.
Therefore, the given numbers do not form an AP.
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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.
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- 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?
- Find the total number of push-ups performed by Nitesh up to the day his goal is achieved.
