Question

Find the common difference, d, given that 8x-3, 4x+1, 2x-2 are consecutive terms of an

arithmetic sequence.
A)1/6
B) -10
C) 10
D) 5

Answer 1

B.) - 10 is the answer.

Explanation:

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Answer 2

B

Explanation:

We are given that:

`8x-3, \, 4x+1, \text{ and } 2x-2`

Are consecutive terms of an arithmetic sequence.

And we want to determine the common difference d.

Recall that for an arithmetic sequence, each subsequent term is d more than the previous term.

In other words, the second term is one d more than the first term. So:

`4x+1=(8x-3)+d`

And the third term is two d more than the first term. So:

`2x-2=(8x-3)+2d`

We can isolate the d in the first equation:

`-4x+4=d`

As well as the second:

`-6x+1=2d\Rightarrow \displaystyle -3x+(1)/(2)=d`

Then by substitution:

`\displaystyle -4x+4=-3x+(1)/(2)`

Solve for x:

`\displaystyle -x=(-7)/(2)\Rightarrow x=(7)/(2)`

The isolated first equation tells us that:

`d=-4x+4`

Therefore:

`\begin{aligned} \displaystyle d&=-4\left((7)/(2)\right)+4\\&=-2(7)+4\\&=-14+4\\&=-10 \end{aligned}`

Our final answer is B.