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You would often see a list of futures prices on stock websites. For example, on Seeking Alpha:

Seeking Alpha futures prices

What are the expiry dates of the futures they are referring to, particularly for the Dow, S&P and Nasdaq futures?

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See if there's "fine print" or a link on the site that tells what the expiry is. There's not a "standard" expiry for futures, so the site should give an indication of what futures contract is used.

CNN Money, for example, list this below the futures quotes:

Futures based on December 2020 contract.

My guess is they use a rolling monthly or quarterly contract to represent a "near-time" futures quote.

It's also possible that the prices are derived from other sources (the link you added shows "Real-Time CFD Derived") or that they are quoting a "fair value" based on one or more actual futures prices. The "fair value" of an index is the discounting of the futures price to the present based on current interest rates and adjusting for dividends. It's supposed to give an indication of what the index should be based on the futures quote.

The bottom line is that there's no "industry standard" for these quotes - without an explanation of the context you're left to speculate.

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