Rose Harrison and Clara Huizink Solutions for Exercise 20: Mixed practice

A sequence has formula $u_n=u_{n-1}-5 \& u_1=12$. Find a formula for the $n^{th}$ term of the sequence.

A sequence has formula $u_{n+1}=u_n+7\text{ \& }{u}_0=15$. Write down the first five terms of the sequence.

A sequence has formula $u_{n+1}=u_n+7\text{ \& }{u}_0=15$. Show that $85$ is a member of the sequene.

A linear sequence begins $18,33,48,\dots$. Find the first term greater than $1000$.

A linear sequence has terms $u_3=6 \& u_6=27$. Find the difference between successive terms.

A linear sequence has terms $u_3=6 \& u_6=27$. Write down the value of $u_7$.

A quadratic sequence begins $3,x,15,25.5,\dots$. Find the value of $x$.

Consider the honeycomb patterns below, which have side length $1,2$and $3$ hexagons respectively.

Find the side length of the first pattern that contains over $1000$ hexagons.