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

In summary, to find the sum of positive integers less than 150 that are not multiples of 5 or 7, first find the sum of all positive integers from 1 to 149. Then, subtract the sum of multiples of 5 from 5 to 145, subtract the sum of multiples of 7 from 7 to 147, and add the sum of multiples of 35 from 35 to 140. This will give you the final answer.
  • #1
Michael_Light
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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...?
 
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  • #2
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.)
 

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

1. What is an arithmetic progression?

An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the common difference, and it remains the same throughout the sequence.

2. How is the common difference calculated in an arithmetic progression?

The common difference in an arithmetic progression can be calculated by subtracting any term from its preceding term. This means that if the first term is 'a' and the second term is 'b', then the common difference is (b-a).

3. What is the formula for finding the nth term in an arithmetic progression?

The formula for finding the nth term in an arithmetic progression is: a + (n-1)d, where 'a' is the first term and 'd' is the common difference.

4. How can you determine if a given sequence is an arithmetic progression?

To determine if a sequence is an arithmetic progression, you can check if the difference between any two consecutive terms is the same. If the difference is constant, then the sequence is an arithmetic progression.

5. How is the sum of an arithmetic progression calculated?

The sum of an arithmetic progression can be calculated using the formula: (n/2)(2a + (n-1)d), where 'a' is the first term, 'd' is the common difference, and 'n' is the number of terms in the sequence.

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