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Find out which of the following sequences are arithmetic progressions. For those which are arithmetic progressions, find out the common difference. 3,6,12,24,......

User Sventechie
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Final answer:

The first sequence 3, 6, 12, 24, ... is not an arithmetic progression as it does not have a constant difference between terms. The last sequence 12.3, 12.4, 12.5, ... is an arithmetic progression with a common difference of 0.1. The remaining sequences need further calculations to determine their status.

Step-by-step explanation:

To determine whether the given sequences are arithmetic progressions (APs), we should look for a constant difference between consecutive terms, known as the common difference. An AP is a sequence where each term after the first is obtained by adding a fixed number, called the common difference, to the previous term.

For the first sequence: 3, 6, 12, 24, ..., we can see that each term is twice the previous term. This means the sequence is not an AP but rather a geometric progression since the ratio (not the difference) between consecutive terms is constant.

For the second and third sequences provided, I would calculate the difference between the successive terms and check for a common difference. If one exists and is consistent throughout, then we have an arithmetic progression. Without performing those calculations, I cannot provide a definitive answer for those sequences with the provided data.

The last sequence: 12.3, 12.4, 12.5, 12.6, ..., clearly shows a constant increase of 0.1 between each term. Therefore, it is an AP with a common difference of 0.1.

User Ivelise
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