Sequences (AQA GCSE Further Maths): Exam Questions

The first four terms of a quadratic sequence are

$010-3$

Work out an expression for the $n$th term.

A linear sequence has first term    $7+12\sqrt{5}$.

The term-to-term rule is

add$9-2\sqrt{5}$

One term of the sequence is an integer.

Work out the value of this integer.

For sequence A,  $n\mathrm{th}$ term = $\frac{n}{14n+30}$.

For sequence B,  $n\mathrm{th}$ term = $\frac{2}{n}$.

The $k\mathrm{th}$ term of sequence A equals the $k\mathrm{th}$ term of sequence B.

Work out the value of $k$. You must show your working.

A quadratic sequence starts

$9,14,23,36,....$

Work out an expression for the $n$th term.

The $n$th term of a sequence is $\frac{2n+1}{n+4}$.

Work out an expression for the difference between the $\left(p+5\right)$th term and the $p$th term.

Give your answer as a single simplified fraction.

Here are the first four terms of linear sequences $X$ and $Y$ and quadratic sequence $Z$.

 Work out the nth term of sequence $X$.

The $n$th term of sequence $Y$ is $3n-1$

Using your answer to part (a), or otherwise, work out the $n$th term of sequence $Z$. Give your answer in the form $a{n}^2+bn+c$ where $a,b$ and $c$ are integers.

The $n$th term of a sequence is $\frac{a{n}^2+5}{b{n}^2+a}$ where $a$ and $b$ are integers.

The second term in the sequence is $\frac{1}{3}$.

The limiting value of the sequence as $n\to \infty$ is $\frac{1}{4}$.

Find the values of $a$ and $b$.

The sequence

$100,36,4,4,36,....$

has an $n$th term formula of $p{\left(2n+q\right)}^2$ where $p$ and $q$ are integers.

Find the values of $p$ and $q$.