How do you write the formula for the nth term given 900, 300, 100, 33 1/3,...?

1 Answer
sente
Apr 2, 2016

#900*(1/3)^(n-1)#

Explanation:

Each term after the first is equal to the previous term multiplied by #1/3#. If we do not simplify at each step, and simply group the #1/3#s together, then we can rewrite the sequence as

#900, 900*1/3, 900*(1/3)^2, 900*(1/3)^3, ...#

and from this it is evident that the #n^"th"# term may be written as #900*(1/3)^(n-1)#.

This type of sequence is called a geometric sequence. A geometric sequence is a sequence of the form #a_0, a_0r, a_0r^2, ...# where #a_0# is the starting term and #r# is the common ratio between terms. In this case, we'd have #a_0 = 900# and #r = 1/3#.

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