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How many three-digit numbers leave a remainder of 2 when divided by 5?

(Such numbers form an AP; use the nth-term formula to count them.)

Class 10nth Term of an APAlgebra — Sequences
  • A180
  • B179
  • C181
  • D178

Step-by-Step Solution

Smallest three-digit number with remainder 2 mod 5 is 102, largest is 997. AP: 102, 107, ..., 997 with d = 5. 997 = 102 + (n-1)5 => 895 = 5(n-1) => n-1 = 179 => n = 180.
Answer: A) 180

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