Question

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

Answer 1

Given:

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

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

`S=(n)/(2)(2a+(n-1)d)`

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

`(6)/(2)(2(-10)+(6-1)d)=-285`

Solve the equation to find (d):

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

So, the answer will be option C) -15