Multiple choice

Find the missing term (?) in the following series: 9, 15, 26, 46, 83, ?

  1. 105

  2. 155

  3. 153

  4. 186

  5. 205
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C Correct answer
Explanation

The differences between consecutive terms are: 15-9=6, 26-15=11, 46-26=20, 83-46=37. The differences of these differences are: 11-6=5, 20-11=9, 37-20=17. The pattern of the second difference is 2*5-1=9, 2*9-1=17, 2*17-1=33. Adding 33 to 37 gives 70. Adding 70 to 83 gives 153.

AI explanation

Calculate the differences between the consecutive terms of the series. The differences are 6, 11, 20, and 37, and their subsequent differences are 5, 9, and 17. The next level of differences is 4 and 8, indicating a geometric progression, so the next difference in this level is 16. Working backward, 17 plus 16 is 33, and adding this to 37 gives a second-level difference of 70; adding 70 to 83 results in 153.

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