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# Algebra and Sequences

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Help?!?!

Find the value of x so that the three given terms are consecutive terms of an arithmetic sequence.

2x – 1, 4x, and 5x + 3

Guest Mar 5, 2017
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2x - 1  is the first term

And we have that  the first term + d  = the second term

2x - 1 + d    = 4x   →   d  = 2x + 1   (1)

And   the first term + 2d  = the third term

2x - 1 + 2d  = 5x + 3  →  2d  = 3x + 4    (2)

Sub (1)  into (2)   and we have that

2 [2x + 1]  = 3x + 4

4x + 2  = 3x + 4       subtract 3x, 2 from both sides

x = 2     and using (1) →  d  = 2(2) + 1   = 5

So

The first term  is 2(2) - 1  = 3

The second term is 4(2)  = 8

And the third term is 5(2) + 3  = 13

Note that the difference between terms = d = 5

CPhill  Mar 5, 2017

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