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26 results.

Identifying different types of sequences
Should not be used
Question in Transition to university by Hannah Aldous and 1 other

Differentiate between linear and quadratic sequences and arithmetic and geometric sequences through a series of multiple choice questions. Spot different patterns in sequences like the triangle sequence, square sequence and cubic sequence and then use this pattern to find the next three terms in each of the sequences.
Find and use the formula for a geometric sequence
Ready to use
Question in Transition to university by Hannah Aldous and 2 others

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.
True/false statements about limits of sequences
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Multiple response question (3 correct out of 6) re properties of convergent and divergent sequences. Selection of questions from a pool.
True/false statements about limits of sequences
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

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.
When does a sequence get within $d$ of its limit?
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

$x_n=\frac{an^2+b}{cn^2+d}$ . Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| < 10 ^{-r},\;n\geq N$ , $2\leq r \leq 6$ . Determine whether the sequence is increasing, decreasing or neither.
Find point when a sequence becomes strictly decreasing
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$x_n=n^k t^n$ 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 $m \geq N$ .
True/false statements about Riemann integration,
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Multiple response question (2 correct out of 4) covering properties of Riemann integration. Selection of questions from a pool.
Find limits of sequences
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Seven standard elementary limits of sequences.
Determine limit of fractional power sequence
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Question on $\displaystyle{\lim_{n\to \infty} a^{1/n}=1}$ . Find least integer $N$ s.t. $\ \left |1-\left(\frac{1}{c}\right)^{b/n}\right| \le10^{-r},\;n \geq N$
Find limit of a sequence
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

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 $|x_n-L| \le 10^{-r},\;n \geq N,\;r \in \{2,\;3,\;4\}$ .
True/false statements about limits of sequences
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

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.
When is a sequence within d of its limit?
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$x_n=\frac{an+b}{cn+d}$ . Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| \le 10 ^{-r},\;n\geq N$ , $2\leq r \leq 6$ .
True/false statements about continuity and differentiability,
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Multiple response question (2 correct out of 4) covering properties of continuity and differentiability. Selection of questions from a pool.

Can choose true and false for each option. Also in one test run the second choice was incorrectly entered, rest correct, but the feedback indicates that the third was wrong.
True/false statements about properties of continuity and limits,
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Multiple response question (2 correct out of 4) covering properties of continuity and limits of functions. Selection of questions from a pool.
Write down and apply the formula for an arithmetic sequence.
Ready to use
Question in Transition to university by Christian Lawson-Perfect

Given the first few terms of an arithmetic sequence, write down its formula, then find a couple of particular terms.
Partial sum of an arithmetic sequence - birthday money
Ready to use
Question in Transition to university by Hannah Aldous and 1 other

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.
Geometric Sequence - negative ratio
Ready to use
Question in Transition to university by Bradley Bush

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.
Finding the formula for the $n^{\text{th}}$ term of linear sequences
Ready to use
Question in Transition to university by Hannah Aldous and 1 other

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.
Finding the $n^{\text{th}}$ Term of a Quadratic Sequence
Ready to use
Question in Transition to university by Hannah Aldous and 2 others

Given the first four terms of a quadratic sequence, write down the formula for the $n^\text{th}$ term.
Find common difference in arithmetic sequences with gaps
Ready to use
Question in Transition to university by Christian Lawson-Perfect

Given sequences with missing terms, find the common difference between terms.
Fill in the gaps in an arithmetic sequence
Ready to use
Question in Transition to university by Christian Lawson-Perfect

Given arithmetic sequences with some terms missing, fill in the missing terms.
Arithmetic sequences in an ice cream shop
Ready to use
Question in Transition to university by Hannah Aldous and 1 other

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.
Compute the partial sum of an arithmetic sequence
Ready to use
Question in Transition to university by Hannah Aldous and 1 other

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.
Sequences and Limits 1.2
Ready to use
Question in Bill's workspace by Bill Foster

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 $|x_n-L| \lt 10^{-r},\;n \geq N,\;r \in \{2,\;3,\;4\}$ .
Sequences and Limits 1.1
Ready to use
Question in Bill's workspace by Bill Foster

Seven standard elementary limits of sequences.
Katie's copy of Sequences and Limits 1.1
Ready to use
Question in Katie's workspace by Katie Dexter

Seven standard elementary limits of sequences.

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