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Select the number from among the given options that can replace the question mark (?) in the following series.
6, 24, 60, 120, 210, ?
336
322
343
432
- The sequence given is 6, 24, 60, 120, 210, and we need to find the next number.
- Notice the pattern: These numbers are formed by a formula involving factorials and triangular numbers.
- The nth term in this sequence is the product of n, (n+1), and (n+2).
- Calculation for the terms:
- 1st term: 1×2×3=6
- 2nd term: 2×3×4=24
- 3rd term: 3×4×5=60
- 4th term: 4×5×6=120
- 5th term: 5×6×7=210
- Next term calculation (6th term): 6×7×8=336
- Among the given options, 336 fits the pattern.
- 336 is the correct answer.
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