Multiple choice

What is the 21st term of the sequence -2, 7, 22, 43,...?

  1. 1218

  2. 1318

  3. 1418

  4. 1518
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B Correct answer
Explanation

Sequence: -2, 7, 22, 43. Differences: 9, 15, 21. Second differences are constant (6). General form: an^2 + bn + c. 2a = 6 => a=3. 3a+b = 9 => 9+b=9 => b=0. a+b+c = -2 => 3+0+c=-2 => c=-5. Term = 3n^2 - 5. 21st term = 3(441) - 5 = 1323 - 5 = 1318.

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