Q3 of 50 Page 26

Prove that for any four consecutive terms of an arithmetic sequence, the sum of the two terms on the two ends and the sum of the two terms in the middle are the same.

Let a,b,c and e are four consecutive terms of an AP with d = common difference.


b = a + d


c = a + 2d


e = a + 3d


First term + Last term = a + e = a + (a + 3d) = 2a + 3d …(1)


Second term + Third term = b + c = (a + d) + (a + 2d) = 2a + 3d …(2)


Hence,


First term + Last term = Second term + Third term


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