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Arithmetic Progressions
Question
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 (i) For what value of p, are 2p – 1,7 and 3p, three consecutive terms of an A . P. ?

(ii) For what value of p are 2p + 1, 13, 5p –3, three consecutive terms of an A . P. ? 

Answer

(i) 2p – 1, 7 and 3p will be three consecutive terms of an A .P. if
Ilnd term – Ist term =IIIrd term – II term
⇒ 7 – (2p – 1) = 3p –7
⇒ 7 – 2p + 1 = 3p – 7
⇒ –2p – 3p = – 7 –8 ⇒ – 5p = – 15
⇒ p = 3.
(ii) 2p + 1, 13 and 5p – 3 will be three consecutive terms of an AP if
13 – (2p + 1) = (5p – 3) – 13
⇒ 13 – 2p – 1 = 5p – 3 – 13
⇒ –2p – 5p = –16 –12
⇒ –7p = –28
⇒ p = 4.

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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, . . .