Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 5.2 ,12 Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms? We know that an = a + (n – 1) d So, 100th term will be a100 = a + (100 – 1) d a100 = a + 99d So, 100th term of 1st AP = a + 99d Let second AP be denoted as bn = b + (n – 1) d b100 = b + (100 – 1) d b100 = b + 99d So, 100th term of 2nd AP = b + 99d As per question , Difference between their 100th terms = 100 a100 – b100 = 100 (a + 99d) – (b + 99d) = 100 a + 99d – b – 99d = 100 a – b + 99d – 99d = 100 a – b = 100 Now we need to find Difference between 1000th terms = a1000 – b1000 = [ a + (1000 – 1)d ] – [ b + (1000 – 1)d] = [ a + 999d ] – [ b + 999d] = a + 999d – b – 999d = a – b + 999d – 999d = a – b Putting value from (1) = 100 So, difference between 1000th terms is 100

Chapter 5 Class 10 Arithmetic Progressions

Serial order wise

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.