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Question
In an AP, the sum of the first term and the last term is equal to the sum of the second term and the second last term and so on.
In an AP, the sum of the first term and the last term is equal to the sum of the second term and the second last term and so on.
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Solution
The correct option is A True
The sum of the first term and the last
the term is equal to the sum of the second
term and the second last term and so on.
To show this, we can take up the
general form of an AP with the terms
as follows:
(a−d),a ,(a+d) (a−2d),(a−d),a ,(a+d),(a+2d) (a−3d),(a−2d),(a−d),a ,(a+d),(a+2d),(a+3d)
Observe that in each of the above
Arithmetic progressions, the sum of
the first term and the last term is equal
to the sum of the second term and the
second last term and so on, which is “2a”.
True
The sum of the first term and the last
the term is equal to the sum of the second
term and the second last term and so on.
To show this, we can take up the
general form of an AP with the terms
as follows:
(a−d),a ,(a+d) (a−2d),(a−d),a ,(a+d),(a+2d) (a−3d),(a−2d),(a−d),a ,(a+d),(a+2d),(a+3d)
Observe that in each of the above
Arithmetic progressions, the sum of
the first term and the last term is equal
to the sum of the second term and the
second last term and so on, which is “2a”.
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