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The sum of the first n terms of the series 9 + 99 + 999 + ... is:

Answer: (10 n+1 − 9n − 10)/9.

  • A (10<sup>n+1</sup> − 9n − 10)/9
  • B (10<sup>n+1</sup> − 10)/9 + n
  • C (10<sup>n+1</sup> − 9n − 10)/81
  • D 10<sup>n+1</sup>/9 − n

Correct answer: A. (10<sup>n+1</sup> − 9n − 10)/9

Explanation: Each term is 10<sup>k</sup> − 1, so the sum is (10<sup>n+1</sup> − 10)/9 − n = (10<sup>n+1</sup> − 9n − 10)/9. Check n = 2: 108.

Each bar grows by the common difference d=3a1=2a2=5a3=8a4=11d=3

Bar heights for AP 2, 5, 8, 11 with the common difference d=3 marked between consecutive terms.

Concept context

Arithmetic progressions, geometric progressions, and sums

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