A series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series.
5 , 11 , 24 , 51 , 106 ,____?
217
This question tests your pattern recognition skills. Let's analyze the given series: 5, 11, 24, 51, 106, __?
Observe the differences between consecutive terms:
- 11 - 5 = 6
- 24 - 11 = 13
- 51 - 24 = 27
- 106 - 51 = 55
Now, let's analyze the differences between these differences:
- 13 - 6 = 7
- 27 - 13 = 14
- 55 - 27 = 28
Notice a pattern? The differences between differences are doubling: 7, 14, 28. The next difference between differences would be 28 * 2 = 56.
Therefore, the next difference between consecutive terms would be 55 + 56 = 111.
Finally, the next term in the original series is 106 + 111 = 217.
Thus, the complete series is: 5, 11, 24, 51, 106, 217.
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