# 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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The nnth term of an arithmetic sequence is ${a}_{n}={a}_{1}+\left(n-1\right)d$ where a_1is the first term and d is the common difference.
For the arithmetic sequence 15, 20, 25, 30, ... the first term is ${a}_{1}=15$ and the common difference is $d={a}_{2}-{a}_{1}=20-15=5$. The nth term is then:
${a}_{n}={a}_{1}+\left(n-1\right)d$
${a}_{n}=15+\left(n-1\right)\left(5\right)$ Substitute.
${a}_{n}=15+5n-5$ Distribute.
${a}_{n}=10+5n$ Combine like terms.

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