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Which of the following is an arithmetic progression?

A. 12.5, 25, 37.5, 50, 62.5
B. 12.5, 25, -12.5, 25, 12.5
C. 12.5, 25, 50, 100, 200

Answer :

Sure! Let's determine which sequence is an arithmetic progression by examining each one:

1. Sequence 1: 12.5, 25, 37.5, 50, 62.5

- First, calculate the difference between consecutive terms:
- [tex]\( 25 - 12.5 = 12.5 \)[/tex]
- [tex]\( 37.5 - 25 = 12.5 \)[/tex]
- [tex]\( 50 - 37.5 = 12.5 \)[/tex]
- [tex]\( 62.5 - 50 = 12.5 \)[/tex]

- Since all differences are the same, the sequence is an arithmetic progression.

2. Sequence 2: 12.5, 25, -12.5, 25, 12.5

- Calculate the difference between consecutive terms:
- [tex]\( 25 - 12.5 = 12.5 \)[/tex]
- [tex]\( -12.5 - 25 = -37.5 \)[/tex]
- [tex]\( 25 - (-12.5) = 37.5 \)[/tex]
- [tex]\( 12.5 - 25 = -12.5 \)[/tex]

- The differences are not the same, so this sequence is not an arithmetic progression.

3. Sequence 3: 12.5, 25, 50, 100, 200

- Calculate the difference between consecutive terms:
- [tex]\( 25 - 12.5 = 12.5 \)[/tex]
- [tex]\( 50 - 25 = 25 \)[/tex]
- [tex]\( 100 - 50 = 50 \)[/tex]
- [tex]\( 200 - 100 = 100 \)[/tex]

- The differences are not the same here either, so this sequence is not an arithmetic progression.

Therefore, the sequence that forms an arithmetic progression is the first one: 12.5, 25, 37.5, 50, 62.5.

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