Which term of the sequence { 16/9, 4/3, 1, 3/4 ... } is 243/1024?

1 Answer
George C.
Dec 26, 2015

The #8#th

Explanation:

This is a geometric sequence with initial term #16/9# and common ratio #3/4#.

The general term of the sequence can be written:

#a_n = 16/9 * (3/4)^(n-1) = (3/4)^(n-3)# for #n = 1, 2, 3,...#

Observe that #243 = 3^5# and #1024 = 2^10 = 4^5#.

Comparing this power with the expression #n - 3#, we find that:

#a_8=243/1024#.

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