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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 term are 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”.
The sum of the first term and the last term are 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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