# Misc 4 - Chapter 9 Class 11 Sequences and Series

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

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.

Miscellaneous

Misc 1

Misc 2

Misc 3 Important

Misc 4 You are here

Misc 5

Misc 6

Misc 7 Important

Misc 8

Misc 9

Misc 10

Misc 11

Misc 12

Misc 13

Misc 14

Misc 15

Misc 16 Important

Misc 17

Misc 18

Misc 19 Important

Misc 20

Misc 21

Misc 22

Misc 23

Misc 24

Misc 25 Important

Misc 26

Misc 27

Misc 28 Important

Misc 29

Misc 30

Misc 31

Misc 32 Important

Chapter 9 Class 11 Sequences and Series

Serial order wise

About the Author

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.