Introduction to sequences

1003085006

Level: 
A
A sequence \( \left(a_n\right)_{n=1}^{\infty} \) is defined by the recursive formula \( a_1=1\text{, }a_2=2;\ a_{n+2} = \frac12\left(a_{n+1}+a_n\right)\text{, }n\in\mathbb{N} \). What are its first five terms?
\( 1 \), \( 2 \), \( \frac32 \), \( \frac74 \), \( \frac{13}8 \)
\( 1 \), \( 2 \), \( \frac32 \), \( \frac47 \), \( \frac8{13} \)
\( 1 \), \( 2 \), \( 3 \), \( 7 \), \( 13 \)
\( 1 \), \( 2 \), \( \frac23 \), \( \frac47 \), \( \frac{13}8 \)

1003085005

Level: 
A
A sequence \( \left( a_n \right)_{n=1}^{\infty} \) is defined by the recursive formula \( a_1=1;\ a_{n+1}=\frac1{1+a_n}\text{, }n\in\mathbb{N} \). What are its first five terms?
\( 1 \), \( \frac12 \), \( \frac23 \), \( \frac35 \), \( \frac58 \)
\( 1 \), \( \frac12 \), \( \frac23 \), \( \frac34 \), \( \frac58 \)
\( 1 \), \( 2 \), \( \frac32 \), \( \frac53 \), \( \frac85 \)
\( 1 \), \( \frac12 \), \( \frac32 \), \( \frac35 \), \( \frac85 \)

1003085004

Level: 
A
A sequence \( \left(a_n\right)_{n=1}^{\infty} \) is defined by the recursive formula \( a_1=1;\ a_{n+1} = 3a_n\text{, }n\in\mathbb{N} \). What are its first five terms?
\( 1 \), \( 3 \), \( 9 \), \( 27 \), \( 81 \)
\( 3 \), \( 9 \), \( 27 \), \( 81 \), \( 243 \)
\( 1 \), \( 3 \), \( 6 \), \( 12 \), \( 24 \)
\( 1 \), \( 3 \), \( 9 \), \( 30 \), \( 90 \)