Is it possible to combine PoW with PoS by taking turns?

Is it possible to combine PoW with PoS by taking turns?

I have read about cryptocurrencies and am very excited by many. I have read that one of the worries and constant debates is Proof of Work vs Proof of State with respect to securing the validity of the blockchain, especially within Ethereum.

I wondered why we would not just combine the two. For example, the first block validated by PoW, second block by PoS, third by PoW, etc. As each block depends on the previous a 51% attack would be a lot more difficult and power consumption significantly reduced.

Is there an obvious problem with doing that?

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