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State Whether the Following Sequence is an A.P. Or Not? 1, 4, 7, 10, …… - Algebra

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प्रश्न

State whether the following sequence is an A.P. or not?

1, 4, 7, 10, ………………..

उत्तर

1, 4, 7, 10, ……
Let ‘d’ be the common difference, ‘a’ be the common ratio, and t2 , t3, t4 be the 2nd, 3rd
and 4th term respectively.
Here t2 = 4, t3 = 7, t4 = 10
d = 4 – 1 = 3
a = 1
We know t2 – a = t3 − t2 = 3
Since the common difference is same throughout the series, therefore the series is an
A.P.

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2014-2015 (March)

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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.


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.

The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

  1. If the first circular row has 30 seats, how many seats will be there in the 10th row?
  2. For 1500 seats in the auditorium, how many rows need to be there?
    OR
    If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after the 10th row?
  3. If there were 17 rows in the auditorium, how many seats will be there in the middle row?

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