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

In summary, we have an arithmetic series with first term 3 and third term 27. The common difference is 12 and the sum of the first 11 terms is 693. For part b, we need to find the sum of all the integers between 50 and 150 that are divisible by 8. To do this, we can make a list of all the numbers between 50 and 150 that are divisible by 8 and notice a pattern. The first number divisible by 8 is 56 and the last number is 144. There are 13 numbers between 50 and 150 that are divisible by 8. The formula for the sum of an arithmetic series is (n/2)(2a +
  • #1
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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??
 
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  • #2
Start making a list of the integers between 50 and 150 which are divisible by 8. Notice anything about this sequence?
 
  • #3
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.
 

1. What is an arithmetic series?

An arithmetic series is a sequence of numbers where the difference between each consecutive term is constant, known as the common difference. For example, the series 2, 5, 8, 11, 14 is an arithmetic series with a common difference of 3.

2. How do you find the sum of an arithmetic series?

The sum of an arithmetic series can be found using the formula S = (n/2)(a + l), where S is the sum, n is the number of terms, a is the first term, and l is the last term. Alternatively, you can also use the formula S = (n/2)(2a + (n-1)d), where d is the common difference.

3. What is the sum of numbers divisible by 8?

The sum of numbers divisible by 8 can be found by using the formula S = (n/2)(a + l), where n is the number of terms, a is the first term (8 in this case), and l is the last term (the largest number divisible by 8 in the given range). Alternatively, you can also use the formula S = (n/2)(2a + (n-1)d), where d is the common difference (also 8 in this case).

4. Can you use the formula for arithmetic series to find the sum of numbers divisible by 8?

Yes, the formula for arithmetic series can be used to find the sum of numbers divisible by 8. This is because the sequence of numbers divisible by 8 is also an arithmetic series with a common difference of 8.

5. How can finding the sum of numbers divisible by 8 be useful?

Finding the sum of numbers divisible by 8 can be useful in many real-life scenarios, such as calculating the total cost of items priced in multiples of 8 or determining the total weight of objects that are measured in multiples of 8. It can also be used in mathematical problems involving divisibility and remainders.

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