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महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

1, 7, 13, 19 ...... find 18th term of this A.P. - Algebra

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प्रश्न

1, 7, 13, 19 ...... find 18th term of this A.P.

बेरीज

उत्तर

The given A.P. is 1, 7, 13, 19, ......

Here, a = 1, d = 7 – 1 = 6

Since tn = a + (n – 1)d,

t18 = 1 + (18 – 1)(6)

= 1 + 17(6)

= 1 + 102

= 103

∴ 18th term of the given A.P. is 103.

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Arithmetic Progression - Q.2 (B)

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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.

If k + 2, 4k – 6 and 3k – 2 are three consecutive terms of an A.P., then the value of k is ______.


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