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Which term in the arithmetic sequence 2x, 3x/2, x,... is -5x/2?

 Jun 26, 2017
 #1
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The common difference is -x/2. Therefore we have the sequence continue as:

 

2x, 3x/2, x, x/2, 0, -x/2, -x, -3x/2, -2x, -5x/2......etc.

And -5x/2 being the 10th term.

 Jun 26, 2017
 #2
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We have: 

-5x/2 = 2x + (N - 1)* -x/2

 

Solve for N:
-(5 x)/2 = 2 x - 1/2 x (N - 1)

-(5 x)/2 = 2 x - 1/2 (N - 1) x is equivalent to 2 x - 1/2 (N - 1) x = -(5 x)/2:
2 x - 1/2 x (N - 1) = -(5 x)/2

Expand out terms of the left hand side:
(5 x)/2 - (N x)/2 = -(5 x)/2

Subtract (5 x)/2 from both sides:
-(N x)/2 = -5 x

Divide both sides by -x/2:
Answer: | N = 10 which is the 10th term of your sequence.

 Jun 26, 2017

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