An arithmetic sequence is a sequence where there is a common difference between any two successive terms.
$$\require{color} \color{red} u_{n} = u_{1}+(n-1)d$$
where $\require{color} \color{red} u_{1}$ is the first term and $\require{color} \color{red}d$ is the common difference of the arithmetic sequence.
Arithmetic Sequence Problems
Example 1
A city is studies and found to have a population of $5000$ in the first year of the study. The population increases by $200$ each year after that.
(a) Write down a rule for the population in month $n$ of the study.
An arithmetic sequence is a sequence where there is a common difference between any two successive terms.
\( \begin{align} \displaystyle
(3x+4)-(x) &= (10x-7)-(3x+4) \\
3x+4-x &= 10x-7 - 3x-4 \\
2x+4 &= 7x-11 \\
2x-7x &= -11-4 \\
-5x &= -15 \\
\therefore x &= 3 \\
\end{align} \)