Question

For an arithmetic series a1 = 10 and s6 = - 285 , find the common difference

Answer 1

step 1: write out the formular for the sum of and Arithmetic series

`\begin{gathered} S_n=(n)/(2)(2a+\text{ (n- 1)d)} \\ \text{where} \\ \text{first term a=-10} \\ \text{ n=6} \\ \\ S_6=-285 \end{gathered}`

Step 2: substitute the values of a,n and S6 in the equation above

`\begin{gathered} -285_{}=(6)/(2)(2*(-10)\text{ +(6 - 1)d} \\ -285=3(-20+5d) \\ -285=-60+15d \\ \\ 15d=-285+60 \\ 15d=-225 \\ d=(-225)/(15) \\ d=-15 \end{gathered}`

Hence the common difference d of the Arithmetic series is d=-15

Therefore the correct answer is option B