# Write a formula for the nth term of the arithmetic sequence 15, 20, 25, 30, ...

Write a formula for the nth term of the arithmetic sequence 15, 20, 25, 30, ...

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casincal
The nth term of an arithmetic sequence is $$\displaystyle{a}_{{{n}}}={a}_{{{1}}}+{\left({n}-{1}\right)}{d}\ {w}{h}{e}{r}{e}\ {a}_{{{1}}}$$ is the first term and d is the common difference.
For the arithmetic sequence 15, 20, 25, 30, ... the first term is $$\displaystyle{a}_{{{1}}}={15}$$ and the common difference is $$\displaystyle{d}={a}_{{{2}}}-{a}_{{{1}}}={20}—{15}={5}$$. The nth term is then
$$\displaystyle{a}_{{{n}}}={a}_{{{1}}}+{\left({n}-{1}\right)}{d}$$
$$\displaystyle{a}_{{{n}}}={15}+{\left({n}-{1}\right)}{\left({5}\right)}$$ Substitute.
$$\displaystyle{a}_{{{n}}}={15}+{5}{n}-{5}$$ Distribute.
$$\displaystyle{a}_{{{n}}}={10}+{5}{n}$$ Combine like terms.