How do you calculate the sum of the arithmetic sequence 8, 14, 20 for 22 terms?

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Calculating the Sum of the Arithmetic Sequence

The arithmetic sequence you provided starts at 8 and has a common difference of 6 (14 – 8 = 6 and 20 – 14 = 6). To find the sum when there are 22 terms, we can use the formula for the sum of an arithmetic sequence:

Sum Formula

The sum S_n of the first n terms of an arithmetic sequence can be calculated using the formula:

S_n = n/2 * (2a + (n – 1)d)

  • n = number of terms
  • a = first term
  • d = common difference

Plugging in the Values

Firstly, we determine the values:

  • n = 22 (the total number of terms)
  • a = 8 (the first term)
  • d = 6 (the common difference)

Inserting these into the formula gives us:

S22 = 22/2 * (2 * 8 + (22 – 1) * 6)

Calculating Step-by-Step

  1. Calculate 22/2: 11.
  2. Calculate (22 - 1) * 6: 21 * 6 = 126.
  3. Calculate 2 * 8 = 16.
  4. Add 16 + 126 = 142.
  5. Finally, compute 11 * 142 = 1562.

The Final Sum

Thus, the sum of the arithmetic sequence 8, 14, 20 for 22 terms is 1562.

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