103 results for "sequence".

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• Question
Falling object used to investigate arithmetic sequence, extension sections relate to geometric sequences and percentage growth.
• Question
Applying an aritmetic sequence to increasing numbers of houses over time, also noting how this can relate to the equation of a straight line and can be given in form y = mt + n.
• Question
From first three terms find common ratio, n for specified u_n  and sum terms.
• Question
Given two (not necessarily consecutive) terms in an arithmetic sequence, evaluate the common difference, first term and then apply to find sum of a number of terms.  (Working with integer terms only)
• Question
Based on first and second term of an arithmetic sequence find common difference and eighth term.
• Question in How-tos

A couple of different ways of showing the correct answer to a single part as soon as the student submits an answer. One way allows the student to change their answer, while the other locks the part.

A third part includes a "reveal answers to this part" button, which allows the student to choose to reveal the answer to the part.

Think very carefully before using this: by revealing the answer, you are removing the opportunity for the student to later on realise they've got that step wrong, as a consequence of some further work. It's often possible to use adaptive marking to use the student's answer in place of the correct answer in later parts.

• Question in How-tos

Given an ascending sequence of numbers, finds the index in the sequence of the first number greater than or equal to a given value.

• Exam (5 questions)

A collection of true/false questions aiming to reveal misconceptions about concepts encountered in a first year pure maths course.

• $x_n=\frac{an^2+b}{cn^2+d}$. 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.

• Question

Multiple response question (4 correct out of 8) covering properties of convergent and divergent series and including questions on power series. Selection of questions from a pool.

• 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.

• Question

$x_n=n^k t^n$ 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 $m \geq N$.

• Question

Question on $\displaystyle{\lim_{n\to \infty} a^{1/n}=1}$. Find least integer $N$ s.t.  $\ \left |1-\left(\frac{1}{c}\right)^{b/n}\right| \le10^{-r},\;n \geq N$

• Question

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 $|x_n-L| \le 10^{-r},\;n \geq N,\;r \in \{2,\;3,\;4\}$.

• Question

Seven standard elementary limits of sequences.

• Question

$x_n=\frac{an+b}{cn+d}$. Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| \le 10 ^{-r},\;n\geq N$, $2\leq r \leq 6$.

• Question

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.

• Question

Multiple response question (3 correct out of 6) re properties of convergent and divergent sequences. Selection of questions from a pool.

• Exam (8 questions)

Questions about the limits of sequences from a first year pure maths course.

• Question

Given the first few terms of an arithmetic sequence, write down its formula, then find a couple of particular terms.

• Question

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.

• Question

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.

• Geometric sequences
Exam (2 questions)

Questions on geometric sequences.

• Question

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.

• Question

Given the first four terms of a quadratic sequence, write down the formula for the $n^\text{th}$ term.

• Question

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.

• Question

Given sequences with missing terms, find the common difference between terms.

• Question

Given arithmetic sequences with some terms missing, fill in the missing terms.

• Question

Given a formula for a sequence, calculate a given term.

• Question

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.