Flag IIT JEE Entrance Exam> Ques. The Sum of the integers from 1 to 1...
question mark

Ques. The Sum of the integers from 1 to 100 which are not divisible by 3 or 5 is(Give solution)

saurabh singh , 10 Years ago
Grade 12th pass
anser 1 Answers
Sourabh Singh

Last Activity: 10 Years ago



Hii

look up the solution to get tyhe approach how to proceed


Sum of all numbers 1 to 100:
S = n[2a1 + (n - 1)d]/2
= 100[2(1) + (100 - 1)]/2
= 100(101)/2
= 5050

Sum of all numbers 3 to 99, multiples of 3:
S = n[2a1 + (n - 1)d]/2
= 33[2(3) + (33 - 1)3]/2
= 33(6 + 96)/2
= 1683

Sum of all numbers 5 to 100, multiples of 5:
S = n[2a1 + (n - 1)d]/2
= 20[2(5) + (20 - 1)5]/2
= 20(10 + 95)/2
= 1050

Sum of all numbers 15 to 90, multiples of 15:
S = n[2a1 + (n - 1)d]/2
= 6[2(15) + (6 - 1)15]/2
= 6(30 + 75)/2
= 315

Sum of integers from 1 to 100 which are not divisible by 3 and 5:
S = sum(1-100) - sum(3-99) - sum(5-100) + sum(15-90)
= 5050 - 1683 - 1050 + 315
= 2632

We have to add in the sum(15-90) because in removing sum(3-99) and sum(5-100), we're taking out multiples of 15 twice. Adding sum(15-90) ensures that we only take out 15 once, 30 once, etc.

Provide a better Answer & Earn Cool Goodies

Enter text here...
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Enter text here...