Question

If n= a +(k-1)d, which of the following gives k in terms of the other variables? 17- A) k= n-at1 k d 72 +a-1 B) k= d n-a-d C) k= d n-ard D) k = d

Answer 1

Isolate k from the given expression:

`n=a+(k-1)d`

Substract a from both sides of the equation:

`\begin{gathered} n-a=a+(k-1)d-a \\ \Rightarrow n-a=(k-1)d \end{gathered}`

Divide both members of the equation by d:

`\begin{gathered} \Rightarrow(n-a)/(d)=((k-1)d)/(d) \\ \Rightarrow(n-a)/(d)=k-1 \end{gathered}`

Add 1 to both sides of the equation:

`\begin{gathered} \Rightarrow(n-a)/(d)+1=k-1+1 \\ \Rightarrow(n-a)/(d)+1=k \\ \end{gathered}`

Write 1 as d/d:

`\begin{gathered} \Rightarrow k=(n-a)/(d)+1 \\ =(n-a)/(d)+(d)/(d) \\ =(n-a+d)/(d) \end{gathered}`

Therefore, the correct answer is displayed in option D:

`k=(n-a+d)/(d)`