2000005807
Level:
A
We are given a sequence with the same difference between consecutive terms. We know it starts at \(-7\) and its \(4\)th term is \(11\). Find its \(12\)th term.
\(59\)
\(53\)
\(65\)
\(71\)
Introduction to sequences
2000005806
Level:
A
In the sequence \( \{-45,-36,-27,-18,\dots\}\) each term can be obtained from previous term by adding \(9\). Which of the following numbers is not a term in the sequence?
\(285\)
\(135\)
\(927\)
\(252\)
2000005805
Level:
A
In the sequence \( \{16,20,24,28,\dots\}\) each term can be obtained from previous term by adding \(4\). Which of the following numbers is not a term in the sequence?
\(322\)
\(200\)
\(40\)
\(764\)
2010005804
Level:
B
We are given a sequence \( \left(\sin \left(n\frac{\pi}{2}\right)\right)^{\infty}_{n=1}\). A part of the sequence is displayed in the graph. Complete the sentence: This sequence is ...
neither increasing nor decreasing.
increasing.
decreasing.
not bounded.
2010005803
Level:
B
We are given a sequence \( (2+(-1)^n)^{\infty}_{n=1}\). A part of the sequence is displayed in the graph. Complete the sentence: This sequence is ...
neither increasing nor decreasing.
increasing.
decreasing.
not bounded.
2010005802
Level:
B
The value of the \(n\)th term of a sequence is given by the expression \(b^{2n}-28\). If the third term of the sequence is \(701\), which of the following is the value of \(b\)?
\(-3\) or \(3\)
\(3\)
\(2\)
\(-3\)
2010005801
Level:
B
The value of the \(n\)th term of a sequence is given by the expression \(a^{4n}-13\). If the second term of the sequence is \(243\), which of the following is the value of \(a\)?
\(-2\) or \(2\)
\(2\)
\(4\)
\(-2\)
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.
\( a_1=2, \ a_{n+1}=-a_n, \ n \in \{1;2;3;4;5\}\)
\( a_1=-2, \ a_{n+1}=-a_n, \ n \in \{1;2;3;4;5\}\)
\( a_1=-2, \ a_{n+1}=-2a_n, \ n \in \{1;2;3;4;5\}\)
\( a_1=2, \ a_{n+1}=a_n, \ n \in \{1;2;3;4;5\}\)
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.
\( a_1=-2, \ a_{n+1}=-a_n, \ n \in \{1;2;3;4;5\}\)
\( a_1=2, \ a_{n+1}=-a_n, \ n \in \{1;2;3;4;5\}\)
\( a_1=-2, \ a_{n+1}=-2a_n, \ n \in \{1;2;3;4;5\}\)
\( a_1=2, \ a_{n+1}=a_n, \ n \in \{1;2;3;4;5\}\)
2010000705
Level:
B
The \(n\)th term of a sequence is given by \(a_n = \frac{n^2-4}{n+4}\). Which term of this sequence is equal to \(5\)?
the eighth term
the third term
the ninth term
the fifth term