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There are many sequences with this property: The sequence with every term equal to 0 has this property. In fact the sequence can be anything you like as long you make sure the 58th term is the sum of the first 10 terms.

A more specific case:

If you are dealing with an arithmetic sequence, i.e. a sequence of the form s(n)=a+bn for constants a and b, we can derive a relationship between a and b:

s(1)+s(2)+...+s(10)=10a+55b

and

s(58)=a+58b

From this, it follows that if s(1)+s(2)+...+s(10)=s(58), then we have 10a+55b=a+58b, which implies that 3a=b. Again, there are infinitely many sequences with this property, but if it is an arithmetic sequence, it will be of the general form s(n)=a+3an=a(3n+1)

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Q: What is the sequence if the sum of the first 10 terms is the same as the 58th term?
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