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Arithmetic Progressions

Question

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For what value of k will k+9, 2k-1 and 2k+7 are the consecutive terms of an A.P?

Solution

If k+9, 2k-1 and 2k+7 are the consecutive terms of A.P, then the common difference will be the same.
∴ (2k – 1) – (k + 9) = (2k + 7) – (2k – 1)

∴ k – 10 = 8

∴ k = 18

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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