Answers to NCERT/CBSE MATH (Class XI)textbook. 9. SEQUENCES AND
SERIES. 5. Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
NCERT/CBSE MATHEMATICS CLASS 11 textbook http://www.TutorBreeze.com MISCELLANEOUS EXERCISES Answers to NCERT/CBSE MATH (Class XI)textbook 9. SEQUENCES AND SERIES
5. Find the sum of integers from 1 to 100 that are divisible by 2 or 5. SOLUTION:
The required AP is 2 , 4, 5, 6, 8,10,..........98,100
( 2 + 4 + 6 + 8 + 10 +... + 100 ) + ( 5 + 15 + 25 + ... + 95 ) ⇒ 2 (1 + 2 + 3 + 4 + 5 +... + 50 ) + 5 (1 + 3 + 5 + ... + 19 ) The required sum of the AP is
n(n+1) 2 50(50+1) 50(51) ⇒ The sum of 50 natural numbers is = 2 2 We know that the sum of n terms of an AP whose The sum of n natural numbers is
First Term = a and Common Difference = d is given by Sn =
n [ 2a + (n − 1)d ] 2
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NCERT/CBSE MATHEMATICS CLASS 11 textbook http://www.TutorBreeze.com
Consider: 1 + 3 + 5 + ... + 19 the sum of n terms of an AP whose First Term = 1 and Common Difference = 3-1 = 2 is given by n [ 2 + (n − 1)2]....(i) 2 We know that the n th term of an Arithmetic Progression, whose
Sn =
First term = a and Common Difference = d is given by an = a + 19 = 1 +
(n - 1 ) d (n - 1 ) 2
⇒ 19 = 1 + 2n - 2 ⇒ 19 =
2n - 1
⇒ 2n = 20 ⇒ n = 10 Putting n in (i) 10 [ 2 + (10 − 1)2] 2 ⇒ S10 = 5 [ 2 + 20 − 2]
