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Example 7 - How many two-digit numbers are divisible by 3?

Example 7 - Chapter 5 Class 10 Arithmetic Progressions - Part 2
Example 7 - Chapter 5 Class 10 Arithmetic Progressions - Part 3


Transcript

Example 7 How many two-digit numbers are divisible by 3? Numbers divisible by 3 are 3, 6, 9, 12, …………….. Lowest two digit number divisible by 3 is 12 Highest two digit number divisible by 3 We know that 99/3 = 33 ∴ Highest two digit number divisible by 3 is 99 So, the series starts with 12 and ends with 99. Difference between numbers is 3 So, the A.P. will be 12, 15, 18, 21, ………….99 We need to find n Last term of this series is 99 So, an = 99 & a = 12 & d = 3 Now, an = a + (n – 1) d Putting values 99 = 12 + (n – 1) (3) 99 = 12 + 3n – 3 99 = 9 + 3n 3n = 99 – 9 3n = 90 n = 90/3 n = 30 Therefore , there are 30 two digit numbers divisible by 3.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.