Sequences

Write down the next two terms in the sequence: $3,\ 7,\ 11,\ 15,\ \ldots$.

Write down the next two terms in the sequence: $2,\ 6,\ 18,\ 54,\ \ldots$.

State whether the sequence $4,\ 8,\ 12,\ 16,\ \ldots$ is arithmetic, geometric, or neither.

For the sequence $15,\ 11,\ 7,\ 3,\ \ldots$, state the common difference $d$.

For the sequence $64,\ 32,\ 16,\ 8,\ \ldots$, state the common ratio $r$.

A sequence begins $7,\ 10,\ 13,\ 16,\ \ldots$. Write down (a) $u_1$ and (b) $u_3$.

A sequence has first term $u_1 = 5$ and term-to-term rule "add $3$". Write down the first four terms.

A sequence has $u_1 = 2$ and term-to-term rule "multiply by $3$". Write down the first four terms.

The $n$th term of a sequence is $u_n = 3n + 2$. Find $u_1$ and $u_5$.

Find the 6th term of the sequence $2,\ 5,\ 8,\ 11,\ \ldots$.

Find the $n$th term formula for the arithmetic sequence $5,\ 8,\ 11,\ 14,\ \ldots$.

Find the $n$th term formula for the sequence $20,\ 17,\ 14,\ 11,\ \ldots$.

For the arithmetic sequence with $u_1 = 7$ and $d = 4$, find $u_{20}$.

For the sequence with $n$th term $u_n = 4n + 1$, find which term equals $81$.

A geometric sequence has $u_1 = 3$ and $r = 2$. Find $u_5$.

A sequence is defined recursively by $u_1 = 4$ and $u_{{n+1}} = u_n + 5$. Find the first four terms.

A sequence is defined by $u_1 = 5$ and $u_{{n+1}} = 2 u_n$. Find $u_4$.

A pattern uses $4$ matchsticks for shape 1, and each new shape adds $3$ more. How many matchsticks for shape 10?

An arithmetic sequence has $u_3 = 11$ and $u_8 = 31$. Find the common difference.

Find the $n$th term formula for the geometric sequence $4,\ 12,\ 36,\ 108,\ \ldots$.

An arithmetic sequence has $u_5 = 17$ and $u_{15} = 47$ where $n = 15$. Find $u_1$ and $d$.

The $n$th term of a sequence is $u_n = 7n + 3$. Find the first term greater than $100$.

A sequence is defined by $u_1 = 5$ and $u_{{n+1}} = 2u_n - 3$. Find $u_4$.

A geometric sequence has $u_2 = 6$ and $u_4 = 54$ (both positive). Find $u_1$ and $r$.

A sequence is given by $1,\ 4,\ 9,\ 16,\ 25,\ \ldots$. Find the next term and describe the pattern.

A sequence is defined by $u_1 = 1$, $u_2 = 2$ and $u_{{n+1}} = u_n + u_{{n-1}}$. Find $u_6$.

Which term of the sequence $u_n = 8n - 5$ equals $99$?

The first three terms of a sequence are $7,\ 4,\ 1,\ -2,\ \ldots$. (a) State the type. (b) Find $u_n$.

Find the sum of the first $10$ terms of the arithmetic sequence with $u_1 = 3$ and $d = 5$.

A geometric sequence has $u_1 = 16$ and $r = \dfrac{1}{2}$. Find $u_4$.

An arithmetic sequence has $u_4 = 14$ and $u_{14} = 44$ where $n = 14$. Find $u_n$ as a formula.

Find the sum of all multiples of $7$ between 1 and $100$ inclusive.

A geometric sequence has $u_3 = 12$ and $u_6 = 96$ (both positive). Find $u_1$ and $r$.

Sequence A has $u_n = 5n + 2$ and sequence B has $u_n = 8n - 7$. For which value of $n$ do they have the same term?

A sequence is defined by $u_1 = 8$ and $u_{{n+1}} = \dfrac{u_n}{2} + 3$. Find $u_4$.

Find the sum of the first $6$ terms of the geometric sequence with $u_1 = 2$ and $r = 3$.

The first four terms of a sequence are $2,\ 6,\ 12,\ 20,\ \ldots$. Find the next term and a quadratic formula for $u_n$.

A bacterial colony of $50$ cells doubles every hour. (a) Write the number of cells $u_n$ after $n$ hours. (b) After how many full hours will the population exceed $1000$?

Maya saves £$5$ in week 1 and £$3$ more each week than the previous week. In which week does her **weekly** saving first exceed £$50$?

A sequence is defined by $u_1 = 1$ and $u_{{n+1}} = u_n + 2n + 1$. Find $u_5$.