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  1. Problems
  2. /Which of these lists are arithmetic progressions? …
EasyMathematicsHigh School (9–10)GeneralAlgebra › Sequences and SeriesConceptualBoard Exam

Which of these lists are arithmetic progressions? …

StemPy LabContributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Which of these lists are arithmetic progressions? Give the common difference of each one that is.

  1. 4,10,16,224, 10, 16, 224,10,16,22 (b) 1,4,9,161, 4, 9, 161,4,9,16 (c) 15,11,7,315, 11, 7, 315,11,7,3 (d) 2.5,2.5,2.5,2.52.5, 2.5, 2.5, 2.52.5,2.5,2.5,2.5
Need a reminder? The key ideaShowHide

An arithmetic progression (AP) adds the same number ddd to each term: a,a+d,a+2d,…a, a + d, a + 2d, \dotsa,a+d,a+2d,… The common difference is a term minus the term before it, and it can be positive, negative or zero. Every difference between neighbouring terms must be equal.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

Step 1. (a) The differences are 6,6,66, 6, 66,6,6. An AP with d=6d = 6d=6.

Step 2. (b) The differences are 3,5,73, 5, 73,5,7. They are not equal, so it is not an AP.

Step 3. (c) The differences are −4,−4,−4-4, -4, -4−4,−4,−4. An AP with d=−4d = -4d=−4.

Step 4. (d) The differences are 0,0,00, 0, 00,0,0. An AP with d=0d = 0d=0.

Answer: (a), (c) and (d) are APs, with d=6d = 6d=6, −4-4−4 and 000; (b) is not.

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