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

1 Answer
George C.
Dec 26, 2015

The 8th

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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