Find the sum of first 28 terms?

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In summary, the given problem is to find the sum of the first 28 terms of an arithmetic progression (AP) where the sum of the first 11 terms is 17 and the sum of the first 17 terms is 11. The formula for finding the sum of an AP is used to solve the equations and determine the values of 'a' and 'd'. While solving, the common difference 'd' may result in a fraction, which is not an error. It can be a whole number, fraction, irrational number, or positive or negative value.
  • #1
nirajnishad
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Homework Statement


sum of first 11 terms of Ap is 17 and sum of first 17 terms is 11
find the sum of first 28 terms?

Homework Equations



Sum=n/2[2a+(n-1)d]

The Attempt at a Solution


i tried solving it by using obove formula but i am not able to do so as the value of d is coming in fraction
 
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  • #2


Just sub in the information and get the values for 'a' and 'd' via solving the equations simultaneously.
 
  • #3


i tried but after soving the equations, value of d is coming in fraction.and the common difference cannot be a fraction number
 
  • #4


nirajnishad said:
i tried but after soving the equations, value of d is coming in fraction.and the common difference cannot be a fraction number

and why not?
 
  • #5


Yes, why cannot the common difference be a fraction? Are 1, 1.25, 1.5, 1.75, 2 not n AP?

Hey Niraj, keep posting your dobts on PF here, we need a lot of warming up to do!
 
  • #6


nirajnishad said:
i tried but after soving the equations, value of d is coming in fraction.and the common difference cannot be a fraction number

The common difference can be a whole number, fraction, irrational number, as well as positive or negative. Finding a fraction most certainly is not an indication of an error on your part.
 

1. What is the formula for finding the sum of the first 28 terms?

The formula for finding the sum of the first n terms in a series is (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term.

2. How do you find the first term in a series?

The first term in a series is typically given or can be calculated using a specific pattern or rule. For example, in an arithmetic series, the first term is the starting number. In a geometric series, the first term is usually given as the initial value or starting value.

3. How do you find the last term in a series?

The last term in a series can be calculated by using the formula an = a + (n-1)d, where an is the last term, a is the first term, n is the number of terms, and d is the common difference between terms in an arithmetic series. In a geometric series, the last term can be found using the formula an = ar^(n-1), where an is the last term, a is the first term, r is the common ratio between terms, and n is the number of terms.

4. Can you use a calculator to find the sum of the first 28 terms?

Yes, you can use a calculator to find the sum of the first 28 terms. Simply plug in the values of the first term, last term, and number of terms into the appropriate formula, and then calculate the result.

5. Why is it important to find the sum of the first 28 terms?

Finding the sum of the first 28 terms is important because it allows us to understand the overall pattern and behavior of a series. It can also help us make predictions about future terms in the series and make calculations more efficient by reducing the number of terms we need to work with.

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