If the sum of the first n terms of an arithmetic series is given by S_n = n/2(2a

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Question: If the sum of the first n terms of an arithmetic series is given by S_n = n/2(2a + (n-1)d), what does \'d\' represent? (2023)

Options:

Correct Answer: Common difference

Exam Year: 2023

Solution:

\'d\' represents the common difference in an arithmetic series.

If the sum of the first n terms of an arithmetic series is given by S_n = n/2(2a + (n-1)d), what does 'd' represent? (2023)

If the sum of the first n terms of an arithmetic series is given by S_n = n/2(2a + (n-1)d), what does 'd' represent? (2023)

Step 1: Understand what an arithmetic series is. It is a sequence of numbers where each term after the first is found by adding a constant value to the previous term.
Step 2: Identify the components of the formula S_n = n/2(2a + (n-1)d). Here, 'S_n' is the sum of the first n terms, 'a' is the first term, and 'n' is the number of terms.
Step 3: Look closely at the term '(n-1)d' in the formula. This part shows how much the terms increase as you go from the first term to the nth term.
Step 4: Recognize that 'd' is the value that is added each time to get from one term to the next. This is called the common difference.
Step 5: Conclude that 'd' represents the common difference in the arithmetic series.

Arithmetic Series – An arithmetic series is a sequence of numbers in which the difference between consecutive terms is constant.
Common Difference – 'd' is the constant difference between consecutive terms in an arithmetic series.
Sum of Terms – The formula provided calculates the sum of the first n terms of an arithmetic series.