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?
\(285\)
\(135\)
\(927\)
\(252\)
Introduction to sequences
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.
\(59\)
\(53\)
\(65\)
\(71\)
2000005809
Level:
A
Which of the following sequences does not contain a term equal to \(256\)?
\(a_n=(-1)^n(n+1)^2\)
\(a_n=\frac{(-2)^n}{n+4}\)
\(a_n = \frac{n^2-516}{n}\)
\( a_n=(-1)^n2^n\)
2000005810
Level:
A
A sequence has \(n\)th term \(3n^2-4n+1\). In the sequence, there are two consecutive terms that sum to \(581\). Find the bigger one of these two terms?
\(320\)
\(11\)
\(261\)
\(10\)
2000010308
Level:
A
A sequence has \(n\)th term \(\frac{1}{3+2n}\) . Which term of the sequence is the first to have the value less than \(\frac1{200}\)?
\( a_{99} \)
\( a_{98} \)
\( a_{101} \)
\( a_{102}\)
2000010309
Level:
A
A sequence has \(n\)th term \(50-\frac{1}{2}n^2\). Which term of the sequence is the first to have the value less than \(0\)?
\( a_{11} \)
\( a_{10} \)
\( a_{6} \)
\( a_{5}\)
2000010310
Level:
A
The \(n\)th term of a sequence is \(\left(\frac12\right)^n\). Find the difference between the \(5\)th and the \(8\)th term of the sequence.
\( \frac{7}{256} \)
\( \frac{3}{128} \)
\(-\frac{7}{256} \)
\( 0\)
2010000401
Level:
A
We are given a sequence \( \left( \frac{n}{n+1} \right)_{n=1}^{\infty} \).
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
2010000403
Level:
A
We are given a sequence \( \left( 5n-3\right)^{\infty}_{n=1} \).
What does this formula express?
a sequence of all natural numbers which after dividing by \(5\) give the remainder \(2\)
a sequence of all natural numbers which are divisible by \(3\)
a sequence of all natural numbers which are divisible by \(5\)
a sequence of all natural numbers which after dividing by \(5\) give the remainder \(3\)
2010000404
Level:
A
Which sequence is defined by the given graph?
\( \left( a_n \right)^{5}_{n=1} = 3,\ \ 2,\ \ 1,\ \ 2,\ \ 3 \)
\( \left( a_n \right)^{10}_{n=1} = 1,\ \ 3,\ \ 2,\ \ 2,\ \ 3,\ \ 1,\ \ 4,\ \ 2,\ \ 5,\ \ 3 \)
\( \left( a_n \right)^{5}_{n=1} = 1,\ \ 2,\ \ 3,\ \ 4,\ \ 5 \)
\( \left( a_n \right)^{5}_{n=1} = 1,\ \ 2,\ \ 2,\ \ 3,\ \ 3 \)