can a geometric sequence have a term equal to zero? yes or no? explain why or why not?

Nth term of a geometric sequence, Tn = ar^(n-1) where a and r are first term and common ratio respectively.

For Tn = 0, a must be 0 or r must be 0 or both, meaning that the rest of the terms will be 0. This makes no sense.

No term can be 0 in a geometric sequence.

Only if it is the geometric sequence 0, 0, 0, 0, ..., which most people would not call a sequence. In a geometric sequence each term is a [non zero] constant times the preceding term. Suppose the tenth term in the sequence was 0. Then the ninth term must have been zero too, because if ka = 0, ither k is zero or a is zero. We know the constant k is not zero, so a must be. And the eighth would be zero, etc., all the way back to the first. And all the following terms would also be zero.

Zero isn't possible. Formula is a*r^(n-1). Imagine a, b, c are in geometric sequence, then r = b/a or c/b. If b is 0, then r is 0 (which doesn't make sense). If a is 0, then b/a is undefined. You can't have common ratio of 0 or an undefined 'fraction' in a geometric sequence