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Find next three terms of the geometric sequence: 400,100,25,dots

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Final answer:

The given sequence is a geometric sequence. By finding the common ratio, we can determine the next terms by multiplying the previous term with the common ratio.

Step-by-step explanation:

The given sequence is: 29, 121, 453, 1,482, 3,466, 6,878, 11,987, 16,162, 20,868, 27,591, 31,335, 36,560, 41,055, 44,730, 49,095, 49,456, 38,510.

  1. The common ratio can be found by dividing any term by its previous term. For example, the common ratio between the second and third terms is 453/121 = 3.75.
  2. To find the next term, multiply the previous term by the common ratio. For example, to find the 17th term, multiply the 16th term (49,456) by the common ratio (3.75).
  3. Repeat the process to find the 18th and 19th terms.

Therefore, the next three terms of the geometric sequence are 49,456 * 3.75 = 185,910, 185,910 * 3.75 = 697,912.5, and 697,912.5 * 3.75 = 2,616,916.25.

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