4.020. Find the first and fifth terms of a geometric progression if it is known that its common ratio is 3, and the sum of the first six terms is 1820.
## Solution.

From the condition, we have $q=3, S_{6}=1820$.

Using formula (4.11), we get $\frac{b_{1}\left(1-3^{6}\right)}{1-3}=1820, b_{1}=5$.

Using formula (4.6), we find $b_{5}=b_{1} q^{4}=5 \cdot(3)^{4}=405$.

Answer: $5,405$.