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Arithmetic Progressions

Question
CBSEENMA10007433
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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.
 –10, –6, –2, 2, ....

Solution

 –10, –6, –2, 2, ....
a2 – a1 = – 6– (–10)
= –6 + 10 = 4
a3 – a2 = –2 – (–6)
= –2 + 6 = 4
a4 – a3 = 2 – (–2)
= 2 + 2 = 4
i.e., ak + 1 – ak is he same every time. So, the given list of numbers forms an A .P. with
the common difference d = 4.
The next three terms are :
2 + 4 = 6, 6 + 4= 10
and 10 + 4 = 14

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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