Introduction to sequences

2010000702

Level: 
B
We are given a sequence \( \left( a_n \right)^{\infty}_{n=1} \) defined recursively by: \( a_1=-1,\ a_2=0\) and \(\ a_{n+2}=a_{n}-a_{n+1}-d\), where \(\ n\in\mathbb{N} \). Find the value of an unknown constant \( d\in\mathbb{R} \) and of the term \( a_5 \) if \( a_3 = -4 \).
\( d=3,\ a_5=-8 \)
\( d=5,\ a_5=-10 \)
\( d=3,\ a_5=1\)
\( d=5,\ a_5=-9 \)

2010000706

Level: 
B
We are given a sequence \( \left( a_n \right)^{6}_{n=1} \) defined by the following graph. Find the recursive formula of such sequence.
\( a_1=-2, \ a_{n+1}=-a_n, \ n \in \{1;2;3;4;5\}\)
\( a_1=2, \ a_{n+1}=-a_n, \ n \in \{1;2;3;4;5\}\)
\( a_1=-2, \ a_{n+1}=-2a_n, \ n \in \{1;2;3;4;5\}\)
\( a_1=2, \ a_{n+1}=a_n, \ n \in \{1;2;3;4;5\}\)

2010000707

Level: 
B
We are given a sequence \( \left( a_n \right)^{6}_{n=1} \) defined by the following graph. Find the recursive formula of such sequence.
\( a_1=2, \ a_{n+1}=-a_n, \ n \in \{1;2;3;4;5\}\)
\( a_1=-2, \ a_{n+1}=-a_n, \ n \in \{1;2;3;4;5\}\)
\( a_1=-2, \ a_{n+1}=-2a_n, \ n \in \{1;2;3;4;5\}\)
\( a_1=2, \ a_{n+1}=a_n, \ n \in \{1;2;3;4;5\}\)