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Calculus/pre cal 12th exponentia and logarithmic functions II


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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