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प्रश्न
In the following situation, involved make an arithmetic progression? and why?
The cost of digging a well after every metre of digging, when it costs Rs 150 for the first metre and rises by Rs 50 for each subsequent metre.
उत्तर
Cost of digging for first metre = 150
Cost of digging for first 2 metres = 150 + 50 = 200
Cost of digging for first 3 metres = 200 + 50 = 250
Cost of digging for first 4 metres = 250 + 50 = 300
Clearly, 150, 200, 250, 300 …
Check:
a = 150
d1 - a2 - a1
= 200 - 150
= 50
d2 = a3 - a2
= 250 - 200
= 50
d3 = a4 - a3
= 300 - 250
= 50
Common difference = 50
Here the common difference is the same hence this series is A.P.
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संबंधित प्रश्न
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If an A.P. consists of n terms with first term a and nth term l show that the sum of the mth term from the beginning and the mth term from the end is (a + l).
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For an A.P., t4 = 12 and its common difference d = – 10, then find tn
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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.
The next term of the A.P. : `sqrt(6), sqrt(24), sqrt(54)` is ______.
Statement A (Assertion): `-5, (-5)/2, 0, 5/2`, .... is in Arithmetic Progression.
Statement R (Reason): The terms of an Arithmetic Progression cannot have both positive and negative rational numbers.
