Statement :

If the first three terms of a sequence are positive, then all of the terms of the sequence are

positive or the sum of the series is positive.

The statement is False.

If the common difference is negative, then it is possible for the first terms to be positive, and the remaining terms to be negative.

So, the sum could also be negative.

Consider the sequence Find the common difference.

Use the common difference of to find the next three terms.

The terms in the sequence are not all positive. 

Find the sum of the first  terms in the sequence.

Therefore the sum is non negative.

The statement is False.