Question

How many integers between 10 and 100 are divisible by 3? Solve by a formula.​

Answer 1

Integers between 10 and 100 that are divisible by 3 are ( 12 , 15 , 18 , . . . ,99 ).

First term ( a ) = 12

Common difference ( d ) = 3

Last lerm ( l ) = 99

Let number of integers divisible by 3 be n . Then

Using AP formula

$l = a + (n - 1)d \\ 99 = 12 + (n - 1) \times 3 \\ 99 = 12 + 3n - 3 \\ 3n = 99 - 12 + 3 \\ 3n = 99 - 9 \\ 3n = 90 \\ n = \frac{90}{3} \\ n = 30$

There are 30 integers between 10 and 100 which are divisible by 3 .

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