1003107402
Level:
B
We were given a sequence \( \left(\frac1{n(n+1)}\right)_{n=1}^{\infty} \).
This sequence is:
decreasing
non-decreasing
increasing
constant
Introduction to sequences
1003107401
Level:
B
We were given a sequence \( \left(\frac{2n+1}{n+2}\right)_{n=1}^{\infty} \).
This sequence is:
increasing
decreasing
non-increasing
constant
1003085010
Level:
A
We were given two sequences \( \left( 2^{2n-2} \right)_{n=1}^{\infty} \) and \( \left( n^2 \right)_{n=1}^{\infty} \).
What is the ratio of their fourth terms?
\( 4:1 \)
\( 2:1 \)
\( 3:1 \)
\( 1:1 \)
1003085009
Level:
A
We were given the sequence \( \left(\frac{n}{n+2}\right)_{n=1}^{\infty} \).
What is its tenth term?
\( \frac56 \)
\( \frac65 \)
\( 1 \)
\( 10 \)
1003085008
Level:
A
A sequence \( \left( a_n \right)_{n=1}^{\infty} \) is defined by the recursive formula: \( a_1=1;\ a_{n+1}=-2a_n\text{, }n\in\mathbb{N} \).
What is its third term?
\( 4 \)
\( 2 \)
\( -4 \)
\( \frac12 \)
1003085007
Level:
A
We were given the sequence \( \left( (-1)^{n+1} \right)_{n=1}^{\infty} \).
What is its seventh term?
\( 1 \)
\( -1 \)
\( 0 \)
\( 2 \)
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?
\( 1 \), \( 3 \), \( 9 \), \( 27 \), \( 81 \)
\( 3 \), \( 9 \), \( 27 \), \( 81 \), \( 243 \)
\( 1 \), \( 3 \), \( 6 \), \( 12 \), \( 24 \)
\( 1 \), \( 3 \), \( 9 \), \( 30 \), \( 90 \)
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?
\( 1 \), \( 0 \), \( -1 \), \( 0 \), \( 1 \)
\( 1 \), \( 0 \), \( 1 \), \( 0 \), \( 1 \)
\( -1 \), \( 0 \), \( 1 \), \( 0 \), \( 1 \)
\( 0 \), \( -1 \), \( 0 \), \( 1 \), \( 0 \)