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

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

2021-02-10
The nnth term of an arithmetic sequence is $$a_{n} = a_{1}+(n-1)d$$ 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:
$$a_{n} = a_{1}+(n - 1)d$$
$$a_{n} = 15 + (n - 1)(5)\$$ Substitute.
$$a_{n} = 15 +5n-5\$$ Distribute.
$$a_{n} = 10 + 5n$$ Combine like terms.

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