Question

Which one of the following is an arithmetic senquence?

Answer 1

Answer:

  D.  -2, 1, 4, 7, 10

Step-by-step explanation:

An arithmetic sequence has a common difference between terms. We can see if the offered choices have that characteristic:

  A. .5 -.35 = .15; .85 -.5 = .35 ≠ .15 . . . . not an arithmetic sequence

  B. 0 -5 = -5; -1 -0 = -1 ≠ -5 . . . . not an arithmetic sequence

  C. 3 -2 = 1; 5 -3 = 2 ≠ 1 . . . . not an arithmetic sequence

  D. 1 -(-2) = 3; 4 -1 = 3; 7 -4 = 3; 10 -7 = 3 . . . . common difference of 3, an arithmetic sequence

The appropriate choice is ...

  D.  -2, 1, 4, 7, 10, ...

Answer 2

Answer:

D. -2, 1, 4, 7, 10, . . .

Step-by-step explanation:

A is incorrect because the common difference is not constant.

B is incorrect because the common difference is not constant.

C is incorrect because the common difference is not constant.

D is the correct answer because the common difference is constant.

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The common difference for the arithmetic sequence -2, 1, 4, 7, 10, . . . is +3 (positive 3). Why? Because -2+3=1; 1+3=4; 4+3=7; 7+3=10; . . . How do you find the common difference to know something is an arithmetic sequence? Well, that part is super easy! All you have to do is subtract each number from the number following it in the sequence. For example, what is the common difference in the following sequence of numbers: {1, 4, 7, 10}? Since the difference is the same for each set, you can say that the common difference is 3 (or positive 3) (+3).  If you get the same common difference for all numbers in the sequence, it is constant, meaning that it is an arithmetic sequence.

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