Question

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.​

Answer 1

Answer:

Let the smallest term be a and the common difference be d.

Then the four consecutive terms are a, a+d, a+2d and a+3d.

The two terms on the end sum up to a+(a+3d) = 2a+3d and the two terms in the middle sum up to (a+d)+(a+2d)=2a+3d. Hence they are the same.

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