How many three-digit numbers are divisible by 9 ?

Foundation

Mathematics Foundation

nth term of AP

Question

100

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Three-digit numbers divisible by 9 are 108, 117, 126, ...... ,999.

Let T_n = 999. Then, 108 + (n – 1) × 9 = 999.

$∴$ (n – 1) × 9 = 891 ⇒ (n – 1) = 99 ⇒ n = 100.