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Misc 4 - Find sum of numbers between 200 and 400 divisible by 7 - Miscellaneous

Misc 4 - Chapter 9 Class 11 Sequences and Series - Part 2
Misc 4 - Chapter 9 Class 11 Sequences and Series - Part 3
Misc 4 - Chapter 9 Class 11 Sequences and Series - Part 4

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Misc 4 Find the sum of all numbers between 200 and 400 which are divisible by 7. Numbers between 200 & 400 are 201, 202,203,… ,398,399 Finding minimum number in 201, 202,203,… ,398,399 which is divisible by 7 201/7 = 285/7 202/7 = 286/7 203/7 = 29 So the series will start from 203 Finding maximum number 201, 202,203,… ,398,399 by 7 399/7 = 57 So the series will end at 399 So, series will start from 203 and end at 399 Thus, all natural number between 200 & 400 which are divisible by 7 are 203, 210, 217, ­­­­­­­­… 392, 399 This sequence forms an A.P. as difference between the consecutive terms is constant. Here first term a = 203 Common difference d = 210 – 203 & last term = l = 399 First we need to find number of terms, i.e. n We know that an = a + (n – 1)d where an = nth term , n = number of terms, a = first term , d = common difference Here, an = last term = l = 399 , a = 203 , d = 7 Putting values 399 = 203 + (n –1) 7 399 – 203 = (n –1) 7 196 = (n –1)7 196/7 = (n –1) 28 = n –1 28 + 1 = n 29 = n n = 29 For finding sum, we use the formula Sn = n/2 [a + l] Here, n = 29 , l = 399& a = 203 S29 = 29/2 (203 + 399) = 29/2 (602) = (29) (301) = 8729 Hence sum of all numbers between 200 to 400 which are divisible by 7 is 8729.

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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.