In the eight term sequence A, B, C, D, E, F, G, H, the value of C is 5

Since C = 5, if we let A = 10, then B must be 15 so that A + B + C = 30. Now D must be 10 so that B + C + D = 30 and E must be 15 so that C + D + E = 30. If we continue the process, we have:

A, B, C, D, E, F, G, and H as 10, 15, 5, 10, 15, 5, 10, and 15, respectively.

Therefore, A + H = 10 + 15 = 25.

(Note: We will leave to readers to try a different number for A and see that, regardless of the choice of the value of A, you will always have A + H = 25.)

Alternate Solution:

Since A + B + C = B + C + D; we have A + B + C - (B + C + D) = A + B + C - B - C - D = A - D = 0; therefore A = D. Applying the same argument, for example for B + C + D = C + D + E, we can conclude B = E and continue in the same way to obtain C = F, D = G and E = H. Since B = E = H, we have

A + B + C = 30

A + H + 5 = 30

A + H = 25

Answer: C

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