Question

find the number of three digit numbers which are divisible by 6 using arithmetic progression step

Answer 1

Step-1: There are 900 three digit positive integers (starting at 100 and up to 999, i.e. 999 - 99) . 900 / 6 = 150, hence, there will be 150 positive three digit numbers (integers) divisible by 6.

Step-2: The first such 3 digit number divisible by 6 is 102.

Answer 2

Answer:

150

Step-by-step explanation:

⇒ Least 3 digit multiple of 6 = 102

⇒ Largest 3 digit multiple of 6 = 996

⇒ As the divisor is 6, the common difference will be 6 if the nos. are in AP.

⇒ Considering the AP,

• → a = 102
• d = 6
• a_n = 996

⇒ To find the no. of terms, use the formula n = (a_n - a)/d + 1.

$\bullet\ n=\frac{a_n-a}{d}+1 \\ \\ \bullet\ n=\frac{996-102}{6}+1 \\ \\ \bullet\ n=\frac{894}{6}+1 \\ \\ \bullet\ n=149+1 \\ \\ \bullet\ n=\bold{150}$

⇒ Thus the answer is 150.