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Algebra

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Let a1, a2, a3, ..., a10 be an arithmetic series. If a1 + a3 = -2 and a2 + a4 + a6 = 1, then find a1.

ChiIIBill Jul 23, 2024

Best Answer

+1950

+1

First, let's set up variables to solve this question.

Let's let $d = a_2 - a_1$

The conditions in the problem give us the system of equations

$\begin{cases} a_1 + d = -1\\ a_1 + 3d = \dfrac13 \end{cases}$

Now, solving this equation, we get that

$d = \dfrac23$ and $a_1 = -\dfrac53$

So the final answer is -5/3.

Thanks! :)

NotThatSmart Jul 23, 2024

edited by NotThatSmart Jul 23, 2024

1⁺⁰ Answers

+1950

+1

Best Answer

First, let's set up variables to solve this question.

Let's let $d = a_2 - a_1$

The conditions in the problem give us the system of equations

$\begin{cases} a_1 + d = -1\\ a_1 + 3d = \dfrac13 \end{cases}$

Now, solving this equation, we get that

$d = \dfrac23$ and $a_1 = -\dfrac53$

So the final answer is -5/3.

Thanks! :)

NotThatSmart Jul 23, 2024

edited by NotThatSmart Jul 23, 2024

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