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algebra senior

Problem

There are two positive numbers that may be inserted between and such that the first three are in geometric progression while the last three are in arithmetic progression. The sum of those two positive numbers is
(A)
(B)
(C)
(D)
Solution
Let be first and be second. We can then get equations based on our knowledge: and . We then get from our first equation and we substitute that into the second to get which simplifies to which be and . Then . Their sum is .
Final answer
B