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.
(b) When will the population double in size?
Example 2
For the arithmetic sequence $\{21,x,y,36\}$, find the values of $x$ and $y$.
Example 3
Find the value of $x$ such that $\{\cdots,x,3x+4,10x-7,\cdots\}$ forms an arithmetic sequence.
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