Answer :
Final answer:
To find the next number in the given number sequence, we must analyze the differences between consecutive numbers. This involves identifying patterns in the first, second, and third differences between the numbers. Following this method, the next number in the series is 288.
Explanation:
The question involves a sequence of numbers and the goal is to identify the pattern to determine the next number in the series. We can observe from the given numbers - 6, 11, 33, 65, 141 - that the difference between each pair of numbers is increasing, indicating a pattern is present.
By examining the differences between consecutive numbers, we deduce the first differences are: 5 (11-6), 22 (33-11), 32 (65-33), and 76 (141-65). No clear pattern emerges from these differences, so we should next examine the second differences.
The second differences are: 17 (22-5), 10 (32-22), and 44 (76-32). Still no clear pattern, so let's move on to the third differences.
The third differences are: -7 (10-17) and 34 (44-10). If we continue this pattern, the next third difference should be 34-7 = 27.
We can then calculate the next second difference by adding this to the previous second difference: 44+27 = 71. The next first difference is then 76+71 = 147. Ultimately, the next number in the series is found by adding this to the previous term: 141+147 = 288.
Learn more about Number Series here:
https://brainly.com/question/35459166
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