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Hi,

Are the following sentences interchangeable? I heard sentence #1 from a native English speaker. I don’t understand why ‘each’ is necessary in this situation.

1. Arithmetic sequences and Geometric sequences are each examples of recurrence sequences.

2. Arithmetic sequences and Geometric sequences are examples of recurrence sequences.

3. Arithmetic sequences and Geometric sequences are an example of recurrence sequences.

Thanks,

MG.
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Hi Musicgold

I would like to advise against drawing conclusions based only on raw search numbers. If you don't bother to look at and analyse the results you get, you will often be misled.

Here is your third sentence again:
3. Arithmetic sequences and Geometric sequences are an example of recurrence sequences.

I have highlighted the word "and" because your sentence in essence provides two different examples. To me, the word "and" itself suggests that the examples are two separate ones. Thus, it would be better to say "are examples".

If you look at your search results more closely, you will find this sort of format:

- German cars are an example of outstanding engineering.

In other words, all of these like things, taken together as a whole, serve as an example of something.
Comments  
Yes, number 1 & 2 are interchangeable. Number 3 is not, as it is grammatically incorrect.

In number 1, the speaker refers to "each" in order to highlight the fact that the two sequences are independent and separate from each other, even though both sequences share something in common.

In number 2, the speaker is highlighting the quantity of sequences (there could be many more but in this instance the speaker has chosen to draw attention to two sequences only). He could have mentioned four or five examples, it doesn't matter. The speaker is more interested in explaining that there is more than just one example of the recurrence sequence.

Number 3 is incorrect because "are an example" mixes plural and singular. You can either have, 'is an example' which would refer to one sequence only, or 'are examples' which would indicate more than one sequence.

However, in this case the first part of the statement mentions two sequences, (plural) therefore only 'are examples' can be used to correct number 3.
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Danny-K,

Thanks a lot
Danny-K Number 3 is incorrect because "are an example" mixes plural and singular.
I remember seeing many native American English speaker using something like this. Even I found it a bit weird initially (my basic English training was based on British English), but looks like Americans are fine with that expression. For example, in the following search from the Google Books site, you will find more than 2000 examples of such a use.

http://books.google.com/books?q=%22are+an+example+of%22

Thanks again,

MG.
 Yankee's reply was promoted to an answer.