Multiple choice

Find the next term of the given series. 17, 18, 27, 52, 101, ?

  1. 182

  2. 192

  3. 172

  4. 158
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The series is 17, 18, 27, 52, 101, ?. The differences are: 18-17=+1, 27-18=+9, 52-27=+25, 101-52=+49. These differences (1, 9, 25, 49) are consecutive odd squares: 1²=1, 3²=9, 5²=25, 7²=49. The next difference should be 9²=81. So 101 + 81 = 182. Therefore option A (182) is correct. Alternatively, each term can be expressed as: n + 2^k + 3^m where k and m increment: 17=16+1, 18=16+2, 27=16+8+3, 52=49+3, 101=64+27+10. The pattern continues to 182.

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