Which number comes next in the series 2, 9, 28, 65, 126, ?

190Correct answerYour answer215Correct answerYour answer216Correct answerYour answer217Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Each term is one more than a cube: $1^3 + 1 = 2$ , $2^3 + 1 = 9$ , $3^3 + 1 = 28$ , $4^3 + 1 = 65$ , $5^3 + 1 = 126$ .
Next term $= 6^3 + 1 = 216 + 1 = 217$ .

Worth noting

216 is $6^3$ without the +1, and 215 subtracts 1 instead. 190 adds $4^3 = 64$ to 126, confusing the cube with the difference (the differences are 7, 19, 37, 61, 91). Numbers just above 8, 27, 64 and 125 are a strong hint of cubes.

Concept: Cubes plus a constant
Typical timeTypical: 70 s
Your timeYours: —

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Which number comes next in the series 2, 9, 28, 65, 126, ?

Explanation