Thursday, September 3, 2015

Please write a conjecture about each pattern and write the next two patterns: Number One: 1/2, 1/4, 1/8. Number Two: -3, 6, -9, 12.

(1)


The given series of
numbers is:


1/2, 1/4, 1/8,
...


This can also be represented
as:


1/(2^1), 1/(2^2), 1/(2^3),
...


Thus the nth term of the series can be represented as
(1/2^n).


Using this formula for the nth term, the first 5
terms of the series become:


1/2, 1/4, 1/8,1/16, 1/32,
...



(2)


The given
series of numbers is:


-3, 6, -9, 12,
...


This can also be represented
as:


(-1^1)(3*1), (-1^2)(3*2), (-1^3)(3*3),
(-1^4)(3*4),...


Thus the nth term of the series can be
represented as (-1^n)(3n).


Using this formula for the nth
term, the first 6 terms of the series become:


-3, 6, -9,
12, -15, 18, ...

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