# Arithmetic Sequence Calculator

## Solve arithmetic progressions step by step

The calculator will find the terms, common difference and sum of the first $n$ terms of the arithmetic sequence from the given data, with steps shown.

Related calculator: Geometric Sequence Calculator

$a($
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$a($
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$S($
$)=$
$S($
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$S($
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$S_{n}$ is the sum of the first $n$ terms.

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Find $a_{7}$, $S_{15}$, given $a_{1} = 5$, $d = 2$.

### Solution

We have that $a_{1} = 5$.

We have that $d = 2$.

$a_{7} = a_{1} + d \left(7 - 1\right) = 5 + 2 \left(7 - 1\right) = 17$

$S_{15} = \frac{2 a_{1} + d \left(15 - 1\right)}{2} \cdot 15 = \frac{\left(2\right)\cdot \left(5\right) + 2 \left(15 - 1\right)}{2} \cdot 15 = 285$

$a_{7} = 17$A
$S_{15} = 285$A