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Arithmetic Progressions

Question
CBSEENMA10007463
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Which of the following are APs? If they form an AP, find the common difference d and write three more terms.
12, 52, 72, 73,....... 




Solution

12, 52, 72, 73,.......
= 52 – 12 = (5 – 1) (5 + 1)
= (4) (6) = 24
a3 – a2 = 72 – 52 = (7 – 5) (7 + 5)
= (2) (12) = 24
a4 – a3 = 73 – 72 = 73 – 49 = 24
i.e., ak + 1 ak is the same every time. So, the given list of numbers forms an A .P. with
the common difference d = 24.
The next three terms are : 73 + 24 = 97 97 + 24 = 121
and 121 + 24 = 145.

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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