Question

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

Answer 1

Answer:

B.) - 10 is the answer.

Step-by-step explanation:

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Answer 2

Answer:

B

Step-by-step 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:

$-6x+1=2d\Rightarrow \displaystyle -3x+\frac{1}{2}=d$

Then by substitution:

$\displaystyle -4x+4=-3x+\frac{1}{2}$

Solve for x:

$\displaystyle -x=\frac{-7}{2}\Rightarrow x=\frac{7}{2}$

The isolated first equation tells us that:

$d=-4x+4$

Therefore:

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

Our final answer is B.