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

#1**+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

#1**+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