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Arithmetic Progressions
Question
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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.

Answer

Cost of digging the well after 1 metre of digging of Rs. 150 = a4
Cost of digging the well after 2 metres of digging
= Rs. 150 + Rs. 50
= Rs. 200 = a2
Cost of digging the well after 3 metres of digging
= Rs. 150 + Rs. 50

= Rs. 2a = a3
Cost of digging the well after 4 metres of digging
= Rs. 200 + Rs. 50
= Rs. 250 = a4
and so on.
a2 – a4 = Rs. 200 – Rs. 150 = Rs. 50
a3 – a2 = Rs. 250 – Rs. 200 = Rs. 50
a4 – a3 = Rs. 350 – Rs. 250 = Rs. 50
i.e., ak +1 – ak is the same every time.
So this list of numbers forms an A .P. with the first term a Rs. 150 and the common difference d = Rs. 50.

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Some More Questions From Arithmetic Progressions Chapter

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, . . .

For the following APs, write the first term and the common difference
0.6, 1.7, 2.8, 3.9, . . .

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
– 1.2, – 3.2, – 5.2, – 7.2, . . .