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Arithmetic Progressions

Question
CBSEENMA10007404
Wired Faculty App

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The amount of air present in a cylinder when a vacuum pump removes 1 fourth of the air remaining in the cylinder at a time.

Solution

Amount of air present in the cylinder = x units (say) = a1
Amount of air present in the cylinder after one time removal of air by the vacuum pump
equals straight x plus straight x over 4 equals fraction numerator 3 straight x over denominator 4 end fraction space units space equals space straight a subscript 2
Amount of air present in the cylinder after two times removal of air by the vacuum pump
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and so on,
straight a subscript 1 minus straight a subscript 1 equals fraction numerator 3 straight x over denominator 4 end fraction minus straight x equals straight x over 4 space units
straight a subscript 3 minus straight a subscript 2 equals open parentheses 3 over 4 close parentheses squared straight x minus 3 over 4 straight x equals fraction numerator 3 straight x over denominator 4 end fraction space units.
As a3 – a7 ≠ a3 – a2, this list of numbers does not form an A .P.

Some More Questions From Arithmetic Progressions Chapter

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a – 10, d = 10

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = –2, d = 0

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = 4, d = – 3

Write first four terms of the AP, when the first term a and the common difference d are given as follows:

a = – 1.25, d = – 0.25

For the following APs, write the first term and the common difference
3, 1, – 1, – 3, . . .

For the following APs, write the first term and the common difference
– 5, – 1, 3, 7, . . .

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