explain: “in an A.P. the sum of terms equidistant from the beginning and end is constant and equal to the sum of first and last term...”

Dear Student,
Let us consider an example of A.P.
1,2,3,4,5,6.
Now The terms which are equidistant from the begining and end will be (1 and 6), (2 and 5), (3 and 4).
Now 2+5 = 3+4 = 1+6 = 7.
I Hope you will get now.
Thanks.

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