Question

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Find the number of all three-digit natural numbers which are divisible by 9. ​

Answer 1

Answer:

All are three digit numbers which are divisible by 9, and thus forms an A.P. having first term a 108 and the common difference as 9. Thus, the number of all three digit natural numbers which are divisible by 9 is 100.

Answer 2

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Find the number of all three-digit natural numbers which are divisible by 9.

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To find: Number of terms of A.P., i.e., n.

A.P. = 108 + 117 + 126 + … + 999

1st term, a = 108

Common difference, d = 117 – 108 = 9

an = 999

a + (n – 1)d = an

∴ 108 + (n – 1) 9 = 999

⇒ (n − 1) 9 = 999 – 108 = 891

⇒ (n − 1) = 891/9 = 99

∴ n = 99 + 1 = 100