Geometric sequences

2010005502

Level: 
B
The sum of the first three terms of a geometric sequence is \( \frac{13}9 \) and the common ratio is \( \frac13 \). Find the sum of all the terms from the \( 3 \)rd to the \( 5 \)th of the sequence.
\( \frac{13}{81} \)
\( \frac{10}{81} \)
\( \frac1{27} \)
\( \frac{40}{81} \)
\( \frac{121}{81} \)

2010005505

Level: 
B
The sum of the first two terms of a geometric sequence is \( 54 \) and its first term equals \( 3 \). Which of the following statements about its common ratio \( q \) is not valid?
\( q \) is an even number.
\( q > 10 \)
\( q < 54 \)
\( q \) is a prime number.
\( q \) is a divisor of \( 51 \).