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question1) which term of the geometric sequence 16, -8, 4, -2...., is the number 1/64?

Lets not worry about the negative sign on every other term.

This series starts at 16, 2^4, and that's the 1st term.

64 is 2^6, so 1/64 is 2^(-6), and that's the last term.

To find out how many terms it takes, take the difference in powers plus 1.

That is, 4 - -6 + 1 = 4 + 6 + 1 = 11.

As far as the negative signs, every even power of 2 is positive, and 1/64 is an even power.

The series would be, counting terms at the end of each line

16 (1),

-8 (2),

4 (3),

-2 (4),

1 (5),

-1/2 (6),

1/4 (7),

-1/8 (8),

1/16 (9),

-1/32 (10),

1/64 (11).

As can be seen, 1/64 is the 11th term.

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