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The problem asks us to find the 5th term (\( U_5 \)) of a geometric sequence, given that:
- The first term (\( a \)) is 5,
- The third term (\( U_3 \)) is 45,
- The common ratio (\( r \)) is positive.

In a geometric sequence, the \( n \)-th term is given by the formula:
\[
U_n = a \cdot r^{n-1}
\]
For the third term (\( U_3 \)):
\[
U_3 = a \cdot r^2
\]
Substituting the known values:
\[
45 = 5 \cdot r^2
\]
Dividing both sides by 5:
\[
r^2 = 9
\]
Taking the positive square root (since \( r \) is positive):
\[
r = 3
\]

Now, we calculate the 5th term (\( U_5 \)):
\[
U_5 = a \cdot r^4 = 5 \cdot 3^4 = 5 \cdot 81 = 405
\]
Multiplying by 3:
\[
U_5 = 5r_

Suku pertama suatu barisan geometri adalah 5 dan U3 = 45. Rasio barisan tersebut positif. S7 barisan tersebut adalah ...

Learn how to find the 7th term of a geometric sequence given the first term (5) and the third term (45) with a positive common ratio. This problem utilizes the nth term formula for geometric sequences, ideal for high school students.

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