Geometric sequences

1003124703

Level: 
A
The second term of a geometric sequence is \( 15 \) and the third term is \( 3 \). Find the recursive formula of the sequence.
\( a_1=75 \), \( a_{n+1} = \frac15a_n \)
\( a_1=3 \), \( a_{n+1} = 5a_n \)
\( a_1=\frac35 \), \( a_{n+1} = \frac15a_n \)
\( a_1=\frac35 \), \( a_{n+1} = 5a_n \)
\( a_1=27 \), \( a_{n+1} = a_n-12 \)

1003124704

Level: 
A
The \( 10 \)th term of a geometric sequence is \( 1 \) and the \( 15 \)th term is \( -1 \). Find the recursive formula of the sequence.
\( a_1=-1 \), \( a_{n+1}=-a_n \)
\( a_1=1 \), \( a_{n+1}=-a_n \)
\( a_1=-1 \), \( a_{n+1}=a_n \)
\( a_1=1 \), \( a_{n+1}=a_n \)
\( a_1=-1 \), \( a_{n+1}=a_n-1 \)

1003124705

Level: 
A
The third term of a geometric sequence is \( 3 \) and the common ratio is \( 3 \). Find the \( n \)th term.
\( a_n=3^{n-2} \), \( n\in\mathbb{N} \)
\( a_n=3^{n-1} \), \( n\in\mathbb{N} \)
\( a_n=3^{n} \), \( n\in\mathbb{N} \)
\( a_n=\frac3n \), \( n\in\mathbb{N} \)
\( a_n=3n \), \( n\in\mathbb{N} \)

1003124706

Level: 
A
The first term of a geometric sequence is \( 5 \) and the fourth term is \( 40 \). Find the \( n \)th term.
\( a_n=5\cdot2^{n-1} \), \( n\in\mathbb{N} \)
\( a_n=\frac{5n}2 \), \( n\in\mathbb{N} \)
\( a_n=5\cdot2^n \), \( n\in\mathbb{N} \)
\( a_n=5n \), \( n\in\mathbb{N} \)
\( a_n=5\cdot\left(2^{n}-1\right) \), \( n\in\mathbb{N} \)

2010004903

Level: 
A
The seventh term of a geometric sequence is \( 32 \) and the tenth term is \( 4 \). Choose the correct formula to find the eighth term of this sequence.
\( a_8=32\cdot\sqrt[3]{\frac4{32}} \)
\( a_8=32\cdot\sqrt[3]{\frac{32}4} \)
\( a_8=4\cdot\sqrt[3]{\frac4{32}} \)
\( a_8=4\cdot\sqrt[3]{\frac{32}4} \)
\( a_8=8\cdot\sqrt[3]{\frac3{24}} \)