- #1
phymatter
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my book says that if sum of p terms of an ARTHMETRIC PROGRESSION is q and sum of q terms is p , then sum of p+q terms will be -(p+q) , but i am getting it as +(p+q),
can someone verify it ?
can someone verify it ?
An arithmetic progression is a sequence of numbers where the difference between consecutive terms is constant. For example, the sequence 2, 5, 8, 11, 14 is an arithmetic progression with a common difference of 3.
Verifying the sum of an arithmetic progression is important because it allows us to check the accuracy of our calculations and ensure that we have not made any errors. It also helps us to understand the pattern and behavior of the sequence.
The sum of an arithmetic progression can be calculated using the formula: Sn = n/2[2a + (n-1)d], where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference.
The confusion arises from the fact that there are two common formulas for calculating the sum of an arithmetic progression. One formula uses the plus sign, while the other uses the minus sign. This can lead to confusion and errors if not specified clearly.
To verify which formula to use, we can check the common difference of the sequence. If the common difference is positive, we use the plus sign formula, and if the common difference is negative, we use the minus sign formula. Alternatively, we can also check the first and last terms of the sequence and see if they are in ascending or descending order.