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Arithmetic Progressions
Question
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A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows : Rs. 200 for 1st day, Rs. 250 for second day, Rs. 300 for third day and so on. If the contractor pays Rs. 27750 as penalty, find the number of days for which the construction work is delayed. 

Answer

Given penalties are, Rs. 200, Rs. 250, Rs. 300 ......
Clearly, it is an arithmetic progression with first term a = 200, common difference d = 50 and Sn = Rs. 27750.

Since, n = –37 is rejected. Hence, the construction work is delayed for 30 days.

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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, . . .