What is the sum of the first 6 terms of the arithmetic series 10, 15, 20, ...?

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Question: What is the sum of the first 6 terms of the arithmetic series 10, 15, 20, ...?

Options:

Correct Answer: 90

Solution:

The sum S_n = n/2 * (2a + (n-1)d) = 6/2 * (2*10 + 5*5) = 3 * (20 + 25) = 135.

What is the sum of the first 6 terms of the arithmetic series 10, 15, 20, ...?

What is the sum of the first 6 terms of the arithmetic series 10, 15, 20, ...?

Step 1: Identify the first term (a) of the series. In this case, a = 10.
Step 2: Identify the common difference (d) of the series. The difference between consecutive terms is 15 - 10 = 5.
Step 3: Identify the number of terms (n) you want to sum. Here, n = 6.
Step 4: Use the formula for the sum of the first n terms of an arithmetic series: S_n = n/2 * (2a + (n-1)d).
Step 5: Substitute the values into the formula: S_6 = 6/2 * (2*10 + (6-1)*5).
Step 6: Calculate 6/2, which equals 3.
Step 7: Calculate 2*10, which equals 20.
Step 8: Calculate (6-1)*5, which equals 5*5 = 25.
Step 9: Add 20 and 25 together to get 45.
Step 10: Multiply 3 by 45 to get the final sum: 3 * 45 = 135.

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