Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ 3n 3S S 2a 3n 1 d S 2 2 1 3 Hence, the given result is proved. [From (3)] Question 4: Find the sum of all numbers between 200 and 400 which are divisible by 7. Solution 4: The numbers lying between 200 and 400, which are divisible by 7, are 203, 210, 217…. 399 First term, I 399 a 203 Last term, Common difference, Let the number of terms of the A.P. be n. d 7 a 399 a n 1 d n 399 203 n 1 7 7 n 1 196 n 1 28 n 29 29 S29 203 399 2 29 602 2 29 301 8729 Thus, the required sum is 8729. Question 5: Find the sum of integers from 1 to 100 that are divisible by 2 or 5. Solution 5: The integers from 1 to 100, which are divisible by 2, are 2, 4, 6 ….. 100. This forms an A.P. with both the first term and common difference equal to 2. 100 2 n 1 2 n 50 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ 50 2 4 6 ...... 100 22 50 12 2 50 4 98 2 25 102 2550 The integers from 1 to 100, which are divisible by 5, 10…. 100. This forms an A.P. with both the first term and common difference equal to 5. 100 5 n 1 5 5n 100 n 20 20 5 10 .... 100 2 5 20 1 5 2 10 10 19 5 10 10 95 10105 1050 The integers, which are divisible by both 2 and 5, are 10, 20, ….. 100. This also forms an A.P. with both the first term and common difference equal to 10. 100 10 n 1 10 100 10n n 10 10 10 20 .... 100 210 10 **11**0 2 5 20 90 5 **11**0 550 Required sum 2550 1050 550 3050 Thus, the sum of the integers from 1 to 100, which are divisible by 2 or 5, is 3050. Question 6: Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder. Solution 6: The two-digit numbers, which when divided by 4, yield 1 as remainder, are 13, 17, …97. This series forms an A.P. with first term 13 and common difference 4. Let n be the number of terms of the A.P. th It is known that the n term of an A.P. is given by, a a n 1 d 97 13 n 1 4 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. n

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