Introduction to sequences

1003084901

Level: 
A
We were given a sequence \( \left( 2n \right)^{\infty}_{n=1} \). What does this formula express?
a sequence of all even natural numbers
a sequence of all natural numbers
a sequence of all odd natural numbers
a sequence of all natural numbers that are divisible by \( 5 \)

1003084902

Level: 
A
We are given a sequence \( \left( 3n-2\right)^{\infty}_{n=1} \). What does this formula express?
a sequence of all natural numbers which after dividing by \( 3 \) give the remainder \( 1 \)
a sequence of all natural numbers which are divisible by \( 3 \)
a sequence of all natural numbers which are divisible by \( 2 \)
a sequence of all odd natural numbers

1003084903

Level: 
A
The table contains ordered pairs of numbers \( [n;a_n] \). \[ \begin{array}{|c|c|c|c|c|c|} \hline n & 1 & 2 & 3 & 4 & 5 \\\hline a_n & -1 & 1 & -2 & 2 & -3 \\\hline \end{array} \] Which sequence is defined by the table?
\( \left(a_n\right)^5_{n=1}=-1\text{, }\ 1\text{, }-2\text{, }\ 2\text{, }-3 \)
\( \left(a_n\right)^{10}_{n=1}=1\text{, }-1\text{, }\ 2\text{, }\ 1\text{, }\ 3\text{, }-2\text{, }\ 4\text{, }\ 2\text{, }\ 5\text{, }-3 \)
\( \left(a_n\right)^5_{n=1}=1\text{, }\ 2\text{, }\ 3\text{, }\ 4\text{, }\ 5 \)
\( \left(a_n\right)^5_{n=1}=0\text{, }\ 3\text{, }\ 1\text{, }\ 6\text{, }\ 2 \)

1003084904

Level: 
A
We were given a sequence \( \left( \frac1n \right)^{\infty}_{n=1} \). Which expression describes the term \( a_{n-1}\ (n\in\mathbb{N}; n>1 ) \) of the given sequence?
\( a_{n-1} = \frac1{n-1} \)
\( a_{n-1} = n-1 \)
\( a_{n-1} = \frac1n \)
\( a_{n-1} = \frac1{2n-1} \)

1003084906

Level: 
A
We are given a sequence \( \left( \frac{n+1}n \right)_{n=1}^{\infty} \). Which of the following formulations describes how is the given sequence defined?
defined by a formula for the \( n \)th term
defined by a list of the sequence elements
defined by a graph of the sequence
defined by a recursive formula for the sequence

1003084907

Level: 
A
A sequence \( \left( a_n \right)^{\infty}_{n=1} \) is defined by the relations: \( a_1=3;\ a_{n+1}=\frac{a_n}{n+2}\text{, }n\in\mathbb{N} \). Which of the following descriptions is used to define the given sequence?
a recursion formula of a sequence
a formula of the \(n\)th term
a list of sequence elements
a graph of a sequence

1003085001

Level: 
A
We were given the sequence \( \left(\frac1{3^n}\right)_{n=1}^{\infty} \). What are its first five terms?
\( \frac13 \), \( \frac19 \), \( \frac1{27} \), \( \frac1{81} \), \( \frac1{243} \)
\( 3 \), \( 9 \), \( 27 \), \( 81 \), \( 243 \)
\( 3 \), \( 6 \), \( 9 \), \( 12 \), \( 15 \)
\( \frac13 \), \( \frac16 \), \( \frac19 \), \( \frac1{12} \), \( \frac1{15} \)

1003085002

Level: 
A
We were given the sequence \( \left(\frac{n+3}{2n}\right)_{n=1}^{\infty} \). What are its first five terms?
\( 2 \), \( \frac54 \), \( 1 \), \( \frac78 \), \( \frac45 \)
\( \frac45 \), \( \frac78 \), \( 1 \), \( \frac54 \), \( 2 \)
\( 2 \), \( \frac45 \), \( 1 \), \( \frac87 \), \( \frac54 \)
\( \frac12 \), \( \frac23 \), \( \frac34 \), \( \frac45 \), \( \frac56 \)

1003085003

Level: 
A
We were given the sequence \( \left(\sin\left(n\cdot\frac{\pi}2\right)\right)_{n=1}^{\infty} \). What are the first five terms?
\( 1 \), \( 0 \), \( -1 \), \( 0 \), \( 1 \)
\( 1 \), \( 0 \), \( 1 \), \( 0 \), \( 1 \)
\( -1 \), \( 0 \), \( 1 \), \( 0 \), \( 1 \)
\( 0 \), \( -1 \), \( 0 \), \( 1 \), \( 0 \)

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?
\( 1 \), \( 3 \), \( 9 \), \( 27 \), \( 81 \)
\( 3 \), \( 9 \), \( 27 \), \( 81 \), \( 243 \)
\( 1 \), \( 3 \), \( 6 \), \( 12 \), \( 24 \)
\( 1 \), \( 3 \), \( 9 \), \( 30 \), \( 90 \)