Find the sum of first 40 positive integers divisible by 6

General
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find the sum of first 40 positive integers divisible by 6

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Find the sum of first 40 positive integers divisible by 6

Answer:
To find the sum of the first 40 positive integers divisible by 6, we can follow these steps:

  1. Identify the Sequence:

    • The series of integers divisible by 6 starts with 6, 12, 18, 24, and so on.
    • This is an arithmetic sequence where the first term a = 6 and the common difference d = 6.

  2. Use the Sum Formula for an Arithmetic Series:

    • The sum of the first n terms of an arithmetic sequence can be calculated using the formula:
      S_n = \frac{n}{2} \cdot (2a + (n-1)d)
    • Here, n = 40, a = 6, and d = 6.

  3. Substitute the Values into the Formula:

    • First, calculate (2a + (n-1)d):
      2a + (n-1)d = 2 \cdot 6 + (40-1) \cdot 6
      2 \cdot 6 + 39 \cdot 6 = 12 + 234 = 246
    • Then, plug this back into the sum formula:
      S_{40} = \frac{40}{2} \cdot 246
      S_{40} = 20 \cdot 246 = 4920

Final Answer:
The sum of the first 40 positive integers divisible by 6 is \boxed{4920}.