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16For an arithmetic series a₁ = -10 and S6 = -285, find the common difference.A-35B-25C -15D -5

Sagot :

Given:

An arithmetic series a₁ = -10 and S6 = -285

We will find the common difference (d) using the formula of the sum.

[tex]S=\frac{n}{2}(2a+(n-1)d)[/tex]

Substitute S= -285, a = -10, n = 6

[tex]\frac{6}{2}(2(-10)+(6-1)d)=-285[/tex]

Solve the equation to find (d):

[tex]\begin{gathered} 3(-20+5d)=-285 \\ -20+5d=-\frac{285}{3} \\ \\ -20+5d=-95 \\ 5d=-95+20 \\ 5d=-75 \\ \\ d=-\frac{75}{5}=-15 \end{gathered}[/tex]

So, the answer will be option C) -15

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