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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 $$$a_{n}$$$, $$$a_{1,2,3,4,5}$$$, $$$a_{7}$$$, $$$S_{15}$$$, given $$$a_{1} = 5$$$, $$$d = 2$$$.
Solution
We have that $$$a_{1} = 5$$$.
We have that $$$d = 2$$$.
The formula is $$$a_{n} = a_{1} + d \left(n - 1\right) = 5 + 2 \left(n - 1\right) = 2 n + 3$$$.
The first five terms are $$$5$$$, $$$7$$$, $$$9$$$, $$$11$$$, $$$13$$$.
$$$a_{7} = a_{1} + d \left(7 - 1\right) = 5 + 2 \left(7 - 1\right) = 17$$$
$$$S_{15} = \frac{2 a_{1} + d \left(15 - 1\right)}{2} \cdot 15 = \frac{\left(2\right)\cdot \left(5\right) + 2 \left(15 - 1\right)}{2} \cdot 15 = 285$$$
Answer
The formula is $$$a_{n} = 2 n + 3$$$A.
The first five terms are $$$a_{1,2,3,4,5} = 5, 7, 9, 11, 13$$$A.
$$$a_{7} = 17$$$A
$$$S_{15} = 285$$$A