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The 10th term counted from the last term of the arithmetic progression 4, 9, 14, …, 254 is:

Competition practiceAlgebra
  • A214
  • B209
  • C204
  • D49

Step-by-Step Solution

Counting backwards from the end turns the progression into one with first term 254 and common difference −5, so the 10th term from the end is . (214 subtracts only 8 steps; 204 subtracts 10 steps instead of 9 — the last term itself is the 1st from the end, not the 0th; 49 is the 10th term from the beginning.) Counting forwards agrees: gives terms, and the 42nd term is .
Answer: B) 209

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