# 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

### Your Input

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

### Solution

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

We have that $$$d = 2$$$.

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

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