What is the sum of the first n terms of the arithmetic series 2, 5, 8, ...?

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Question: What is the sum of the first n terms of the arithmetic series 2, 5, 8, ...?

Options:

Correct Answer: n/2 * (2 + (n-1) * 3)

Solution:

The first term a = 2, common difference d = 3. The sum of the first n terms S_n = n/2 * (2a + (n-1)d) = n/2 * (2 + (n-1) * 3).

What is the sum of the first n terms of the arithmetic series 2, 5, 8, ...?

What is the sum of the first n terms of the arithmetic series 2, 5, 8, ...?

Step 1: Identify the first term of the series. The first term (a) is 2.
Step 2: Identify the common difference of the series. The common difference (d) is 5 - 2 = 3.
Step 3: Write the formula for the sum of the first n terms of an arithmetic series: S_n = n/2 * (2a + (n-1)d).
Step 4: Substitute the values of a and d into the formula: S_n = n/2 * (2*2 + (n-1)*3).
Step 5: Simplify the expression: S_n = n/2 * (4 + (n-1)*3).
Step 6: Further simplify: S_n = n/2 * (4 + 3n - 3) = n/2 * (3n + 1).

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