Mean sequence

Weekly Problem 38 - 2009
This sequence is given by the mean of the previous two terms. What is the fifth term in the sequence?
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Problem



The first two terms of a sequence are $\frac{2}{3}$ and $\frac{4}{5}$.

Each subsequent term is the mean of the two previous terms.

What is the fifth term in the sequence?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.