What is the next term in this geometric sequence?
\[
\frac{5}{6}, \frac{5}{9}, \frac{10}{27}, \frac{20}{81}
\]
Answer (3)
a 1 = 6 5 ; a 2 = 9 5 ; a 3 = 27 10 ; a 4 = 81 20 q = a 2 : a 1 q = 9 5 : 6 5 = 9 5 ⋅ 5 6 = 3 2 a 5 = a 4 ⋅ q a 5 = 81 20 ⋅ 3 2 = 243 40 → an s w er
(20/81) * (2/3) = 40/243;
the next term in this geometric sequence is 40/243.
The next term in the given geometric sequence is 243 40 . This was found by determining the common ratio, which is 3 2 , and applying it to the last term. By following through the steps, we confirmed that each term consistently followed this ratio.
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