114 results for "sequence".
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Exam (5 questions) in Content created by Newcastle University
A collection of true/false questions aiming to reveal misconceptions about concepts encountered in a first year pure maths course.
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Question in Content created by Newcastle University
$x_n=n^k t^n$ where $k$ is a positive integer and $t$ a real number with $0 < t<1$. Find the smallest integer $N$ such that $(m+1)^k t^{m+1} \leq m^k t^m$ for all $m \geq N$.
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Question in Content created by Newcastle University
Multiple response question (4 correct out of 8) covering properties of convergent and divergent sequences and boundedness of sets. Selection of questions from a pool.
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Question in Content created by Newcastle University
Let $x_n=\frac{an+b}{cn+d},\;\;n=1,\;2\ldots$. Find $\lim_{x \to\infty} x_n=L$ and find least $N$ such that $|x_n-L| \le 10^{-r},\;n \geq N,\;r \in \{2,\;3,\;4\}$.
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Question in Content created by Newcastle University
Seven standard elementary limits of sequences.
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Question in Content created by Newcastle University
$x_n=\frac{an+b}{cn+d}$. Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| \le 10 ^{-r},\;n\geq N$, $2\leq r \leq 6$.
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Exam (8 questions) in Content created by Newcastle University
Questions about the limits of sequences from a first year pure maths course.
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Question in Content created by Newcastle University
Question on $\displaystyle{\lim_{n\to \infty} a^{1/n}=1}$. Find least integer $N$ s.t. $\ \left |1-\left(\frac{1}{c}\right)^{b/n}\right| \le10^{-r},\;n \geq N$
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Question in Transition to university
Given the first few terms of an arithmetic sequence, write down its formula, then find a couple of particular terms.
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Question in Transition to university
The amount of money a person gets on their birthday follows an arithmetic sequence.
Calculate the amount on a given birthday, then calculate the sum up to that point.
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Exam (2 questions) in Transition to university
Questions on geometric sequences.
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Question in Transition to university
Given a geometric sequence, find the common ratio (negative in this question), write down the formula for the nth term and use it to calculate a given term.
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Question in Transition to university
Given the first four terms of a quadratic sequence, write down the formula for the $n^\text{th}$ term.
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Question in Transition to university
Given the first three terms of a sequence, give a formula for the $n^\text{th}$ term.
In the first sequence, $d$ is positive. In the second sequence, $d$ is negative.
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Question in Transition to university
Given sequences with missing terms, find the common difference between terms.
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Question in Transition to university
Given arithmetic sequences with some terms missing, fill in the missing terms.
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Question in Transition to university
Given a formula for a sequence, calculate a given term.
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Question in Transition to university
Given the first and last terms of a finite arithmetic sequence, calculate the number of elements and then the sum of the sequence.
Each part is broken into steps, with the formula given.
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Question in Transition to university
Given the common difference and first term of an arithmetic sequence, work out the index of the nth term of the sequence.
Framed as a word problem with ticket numbers in an ice cream shop.
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Exam (7 questions) in Transition to university
Questions on arithmetic, or linear, sequences.
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Question in Leonardo's workspace
Multiple response question (3 correct out of 6) re properties of convergent and divergent sequences. Selection of questions from a pool.
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Question in College Algebra for STEM
Given a geometric sequence, find the common ratio (negative in this question), write down the formula for the nth term and use it to calculate a given term.
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Question in College Algebra for STEM
Given the first four terms of a quadratic sequence, write down the formula for the $n^\text{th}$ term.
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Question in College Algebra for STEM
Given a formula for a sequence, calculate a given term.
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Question in College Algebra for STEM
Given the first three terms of a sequence, give a formula for the $n^\text{th}$ term.
In the first sequence, $d$ is positive. In the second sequence, $d$ is negative.
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Question in College Algebra for STEM
Given the common difference and first term of an arithmetic sequence, work out the index of the nth term of the sequence.
Framed as a word problem with ticket numbers in an ice cream shop.
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Question in College Algebra for STEM
The amount of money a person gets on their birthday follows an arithmetic sequence.
Calculate the amount on a given birthday, then calculate the sum up to that point.
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Question in College Algebra for STEM
Given the first and last terms of a finite arithmetic sequence, calculate the number of elements and then the sum of the sequence.
Each part is broken into steps, with the formula given.
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Question in College Algebra for STEM
Given sequences with missing terms, find the common difference between terms.
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Question in College Algebra for STEM
Given arithmetic sequences with some terms missing, fill in the missing terms.