Sum of Positive Integers Less Than 150 Not Multiples of 5 or 7

Click For Summary
SUMMARY

The task is to calculate the sum of positive integers less than 150 that are not multiples of 5 or 7. The solution involves four steps: first, calculate the sum of integers from 1 to 149; second, compute the sum of multiples of 5 up to 145; third, find the sum of multiples of 7 up to 147; and fourth, determine the sum of multiples of 35 up to 140. The final result is obtained by applying the formula A - B - C + D, where A, B, C, and D represent the respective sums calculated.

PREREQUISITES
  • Understanding of arithmetic series and their sums
  • Knowledge of multiples and least common multiples (LCM)
  • Basic algebraic manipulation skills
  • Familiarity with mathematical notation and summation
NEXT STEPS
  • Study the formula for the sum of an arithmetic series
  • Learn how to calculate least common multiples (LCM) effectively
  • Explore the concept of inclusion-exclusion in set theory
  • Practice similar problems involving sums and multiples
USEFUL FOR

Students in mathematics, educators teaching arithmetic series, and anyone interested in problem-solving techniques related to number theory.

Michael_Light
Messages
112
Reaction score
0

Homework Statement



Find the sum of the positive integers which are less than 150 and are not multiples of 5 or 7.


Homework Equations





The Attempt at a Solution



I tried it... Can anyone give me some hints or tips...?
 
Physics news on Phys.org
Find:
A) The sum of the positive integers from 1 to 149,
B) The sum of the multiples of 5 from 5 to 145,
C) The sum of the multiples of 7 from 7 to 147,
D) The sum of the multiples of 35 from 35 to 140.

Then, your final answer will be A - B - C + D. (We have to add the answer in D because by subtracting the answers in B and C, we are removing the multiples of 35 twice.)
 

Similar threads

Find α+β+αβ: 7 "Solving for α+β+αβ in Arithmetic Progression
  • · Replies 24 ·
Replies
24
Views
4K
Question about arithmetic progressions
  • · Replies 3 ·
Replies
3
Views
2K
Set properties of even (##E##) and odd (##I##) integers
  • · Replies 5 ·
Replies
5
Views
2K
Arithmetic Progression: Find Common Difference with Given First Term and Ratio
  • · Replies 3 ·
Replies
3
Views
2K
What Is the Common Difference in This Arithmetic Progression?
  • · Replies 3 ·
Replies
3
Views
2K
Solving Arithmetic Progression: Sum and Product of Four Integers
  • · Replies 4 ·
Replies
4
Views
2K
Prime Number Arithmetic Progression
  • · Replies 5 ·
Replies
5
Views
4K
Arithmetic Progression Problem
  • · Replies 2 ·
Replies
2
Views
2K
Solving for the Sum of an Arithmetic Progression | m>n | AP Homework
  • · Replies 4 ·
Replies
4
Views
2K
Arithmetic Progression: Finding the Sum of Terms with Given Conditions
  • · Replies 2 ·
Replies
2
Views
3K