Multiple choice

Directions: Find the next term of the given series. 12, 34, 74, 138, ____

  1. 192

  2. 202

  3. 212

  4. 232

  5. 264
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Differences: 34-12=22, 74-34=40, 138-74=64. Second differences: 40-22=18, 64-40=24. The second difference increases by 6. Next second difference is 30. Next first difference is 64+30=94. Next term is 138+94=232.

AI explanation

The differences between the consecutive terms are squares of consecutive even numbers. The difference between 34 and 12 is 22, between 74 and 34 is 40, and between 138 and 74 is 64. These differences represent 4 squared, 6 squared, and 8 squared, so the next difference must be 10 squared, which is 100. Adding 100 to 138 gives the next term as 232.

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