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

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 'a' 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 'a' 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 difference (d) to the previous term.
Step 2: Identify the formula given: S_n = n/2(2a + (n-1)d). This formula calculates the sum of the first n terms of the arithmetic series.
Step 3: Look at the components of the formula. 'n' is the number of terms, 'd' is the common difference, and 'a' is a variable in the formula.
Step 4: Recognize that in the context of the formula, 'a' is used to represent the first term of the arithmetic series.
Step 5: Conclude that 'a' is the starting point of the series from which all other terms are derived.

Arithmetic Series – An arithmetic series is the sum of the terms of an arithmetic sequence, where each term is generated by adding a constant difference to the previous term.
Sum of Terms Formula – The formula S_n = n/2(2a + (n-1)d) is used to calculate the sum of the first n terms of an arithmetic series, where 'a' is the first term and 'd' is the common difference.