Arithmetic Sequence Calculator

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.

`a`()`=`

`a`()`=`

`a`()`=`

Common difference `d=`

Sum of the first terms `S`()`=`

Sum of the first terms `S`()`=`

Sum of the first terms `S`()`=`

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Solution

Your input: find $$$a_{7}$$$, the sum of the first $$$15$$$ terms, given $$$a_{1}=5$$$, the common difference $$$d=2$$$.

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

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

Finally,

$$$a_{7}=a_1+d\left(7 - 1\right)=5+\left(2\right)\left(7 - 1\right)=17$$$.

$$$S_{15}=\frac{2a_1+d\left(15 - 1\right)}{2}{15}=\frac{2\left(5\right)+\left(2\right)\left(15 - 1\right)}{2}{15}=285$$$.

Answer

$$$a_{1}=5$$$.

$$$a_{7}=17$$$.

The common difference is $$$d=2$$$.

$$$S\left(15\right)=285$$$.