Find Sum of Arithmetic Series & Sum of Numbers Divisible by 8

  • Thread starter Thread starter discombobulated
  • Start date Start date
  • Tags Tags
    Arithmetic Series
Click For Summary
SUMMARY

The discussion focuses on solving two mathematical problems: finding the common difference and sum of an arithmetic series, and calculating the sum of integers divisible by 8 within a specified range. The common difference of the arithmetic series, with first and third terms as 3 and 27, is determined to be 12, leading to a total sum of the first 11 terms as 693. For the second part, participants are guided to identify integers between 50 and 150 that are divisible by 8, emphasizing the importance of recognizing the first and last terms in the sequence to facilitate the calculation of their sum.

PREREQUISITES
  • Understanding of arithmetic series and their properties
  • Ability to calculate common differences in sequences
  • Knowledge of divisibility rules, specifically for the number 8
  • Familiarity with summation formulas for sequences
NEXT STEPS
  • Learn how to derive the formula for the sum of an arithmetic series
  • Explore methods for identifying terms in a sequence based on divisibility
  • Study the application of the arithmetic series sum formula in practical scenarios
  • Investigate the properties of sequences and series in number theory
USEFUL FOR

Students, educators, and anyone interested in enhancing their understanding of arithmetic series and number theory, particularly those tackling problems involving sequences and divisibility.

discombobulated
Messages
41
Reaction score
0
8a) The first and third terms of an arithmetic series are 3 and 27 respectively.
i) find the common difference
ii) find the sum of the first 11 terms of the series
b) find the sum of the inteers between 50 and 150 which are divisible by 8.
I have already done part a) and found the common difference to be 12 and the sum of the first 11 terms to be 693.
But i have no idea how to start part b, any suggestions please??
 
Physics news on Phys.org
Start making a list of the integers between 50 and 150 which are divisible by 8. Notice anything about this sequence?
 
What is the first number, larger than or equal to 50, that is divisible by 8.
What is the last number, less than or equal to 150, that is divisible by 8?

How many numbers are the between 50 and 150 that are divisible by 8 (after you answer the first two questions, this is easy.)

Is there a formula for the sum? Hint: the title of this thread.
 

Similar threads

Finding a and d from the Sum of an Arithmetic Series
  • · Replies 2 ·
Replies
2
Views
2K
Solving for the Sum of an Arithmetic Progression | m>n | AP Homework
  • · Replies 4 ·
Replies
4
Views
2K
Divisibility Test: Determine if a Number is Divisible by 6, 8, 4
  • · Replies 7 ·
Replies
7
Views
2K
Middle Terms in an Arithmetic Series
  • · Replies 6 ·
Replies
6
Views
2K
Sum of Infinite Series: Finding the Value of S
  • · Replies 10 ·
Replies
10
Views
3K
How to Solve Problems in Arithmetic Series Using Formulas?
  • · Replies 2 ·
Replies
2
Views
2K
Finding sum of infinite series
  • · Replies 14 ·
Replies
14
Views
3K
Sum of range of numbers divisble by 6 but not by 9
  • · Replies 4 ·
Replies
4
Views
2K
Values of x for which a geometric series converges
  • · Replies 1 ·
Replies
1
Views
5K
Finding the First Term and Common Difference of an Arithmetic Series
  • · Replies 1 ·
Replies
1
Views
2K