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Calculus/pre cal 12th exponentia and logarithmic functions II


question 1) what is the 10th term of the following sequence?
16, 4,1....

question 2) use sigma notation to write the sum of the following series
4+20+100+500+2500+12 5000

Answer to question 1)  the sequence is 16, 4, 1, 1/4, 1/16, 1/64, 1/2561/1024, 1/4096, 1/16384, ...
So the tenth term is 1/16384.

Answer to question 2)  the terms seem to follow a geometric pattern.  The next term is 5 times the previous term.  So in sigma notation (I hope you know how to write the big sigma to denote SUM, with tiny indication on the top and bottom telling people where n is starting and where it is ending), it is sum_{n=0}^{infinity}  4*5^n


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