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Question

Arrange the APs in the increasing order of their common differences (top to bottom).

A
4, -1, -6, -11..
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B
4, 1, -2, -5..
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C
5, 4, 3, 2 ..
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D
7, 9, 11, 13..
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E
7, 11, 15, 19..
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Solution

The common difference of an AP is the difference between any two consecutive terms of the AP.

In the AP 4, -1, -6, -11,...
a1=4 and a2=1.
But, d=a2a1=14=5.

In the AP 5, 4, 3, 2, ...
a1=5 and a2=4.
But, d=a2a1=45 =1.

In the AP 7, 9, 11, 13, ...
a1=7 and a2=9.
But, d=a2a1=97=2.

In the AP 7, 11, 15, 19, ...
a1=7 and a2=11.
But, d=a2a1=117=4.

In the AP 4, 1, -2, -5, ...
a1=4 and a2=1.
But, d=a2a1=14=3.

Since 5<3<1<2<4, we have the required order.

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