Sequences

Write down the next two terms in the sequence: $5,\ 9,\ 13,\ 17,\ \ldots$.

Write down the next two terms in the sequence: $3,\ 12,\ 48,\ 192,\ \ldots$.

State whether the sequence $1,\ 2,\ 4,\ 8,\ \ldots$ is arithmetic, geometric, or neither.

For the sequence $20,\ 14,\ 8,\ 2,\ \ldots$, state the common difference $d$.

For the sequence $81,\ 27,\ 9,\ 3,\ \ldots$, state the common ratio $r$.

A sequence begins $12,\ 18,\ 24,\ 30,\ \ldots$. Write down (a) $u_1$ and (b) $u_3$.

A sequence has first term $u_1 = 2$ and term-to-term rule "add $7$". Write down the first four terms.

A sequence has $u_1 = 5$ and term-to-term rule "multiply by $2$". Write down the first four terms.

The $n$th term of a sequence is $u_n = 4n + 1$. Find $u_1$ and $u_5$.

Find the 6th term of the sequence $7,\ 12,\ 17,\ 22,\ \ldots$.

Find the $n$th term formula for the arithmetic sequence $3,\ 9,\ 15,\ 21,\ \ldots$.

Find the $n$th term formula for the sequence $50,\ 45,\ 40,\ 35,\ \ldots$.

For the arithmetic sequence with $u_1 = 12$ and $d = 3$, find $u_{25}$.

For the sequence with $n$th term $u_n = 5n + 2$, find which term equals $102$.

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

A sequence is defined recursively by $u_1 = 1$ and $u_{{n+1}} = u_n + 6$. Find the first four terms.

A sequence is defined by $u_1 = 4$ and $u_{{n+1}} = 3 u_n$. Find $u_4$.

A pattern uses $5$ matchsticks for shape 1, and each new shape adds $4$ more. How many matchsticks for shape 10?

An arithmetic sequence has $u_3 = 9$ and $u_8 = 24$. Find the common difference.

Find the $n$th term formula for the geometric sequence $5,\ 10,\ 20,\ 40,\ \ldots$.

An arithmetic sequence has $u_5 = 14$ and $u_{15} = 44$ where $n = 15$. Find $u_1$ and $d$.

The $n$th term of a sequence is $u_n = 5n + 2$. Find the first term greater than $200$.

A sequence is defined by $u_1 = 4$ and $u_{{n+1}} = 2u_n - 2$. Find $u_4$.

A geometric sequence has $u_2 = 8$ and $u_4 = 32$ (both positive). Find $u_1$ and $r$.

A sequence is given by $1,\ 8,\ 27,\ 64,\ \ldots$. Find the next term and describe the pattern.

A sequence is defined by $u_1 = 2$, $u_2 = 3$ and $u_{{n+1}} = u_n + u_{{n-1}}$. Find $u_6$.

Which term of the sequence $u_n = 6n - 1$ equals $89$?

The first three terms of a sequence are $10,\ 6,\ 2,\ -2,\ \ldots$. (a) State the type. (b) Find $u_n$.

Find the sum of the first $12$ terms of the arithmetic sequence with $u_1 = 2$ and $d = 3$.

A geometric sequence has $u_1 = 81$ and $r = \dfrac{1}{3}$. Find $u_4$.

An arithmetic sequence has $u_4 = 11$ and $u_{14} = 41$ where $n = 14$. Find $u_n$ as a formula.

Find the sum of all multiples of $5$ between 1 and $200$ inclusive.

A geometric sequence has $u_3 = 18$ and $u_6 = 486$ (both positive). Find $u_1$ and $r$.

Sequence A has $u_n = 5n + 2$ and sequence B has $u_n = 7n - 6$. For which value of $n$ do they have the same term?

A sequence is defined by $u_1 = 12$ and $u_{{n+1}} = \dfrac{u_n}{2} + 2$. Find $u_4$.

Find the sum of the first $5$ terms of the geometric sequence with $u_1 = 3$ and $r = 2$.

The first four terms of a sequence are $3,\ 8,\ 15,\ 24,\ \ldots$. Find the next term and a quadratic formula for $u_n$.

A bacterial colony of $100$ 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 $5000$?

Maya saves £$4$ in week 1 and £$2$ more each week than the previous week. In which week does her **weekly** saving first exceed £$40$?

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