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Find the sum of the first 5 terms of the infinite series 8 + 18 + 28 + ...

User RobertT
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Final answer:

To find the sum of the first 5 terms of the arithmetic series 8 + 18 + 28 + ..., we identify the common difference as 10 and calculate the sum of 8, 18, 28, 38, and 48, resulting in a total of 140.

Step-by-step explanation:

The question is asking for the sum of the first 5 terms of the arithmetic series 8 + 18 + 28 + ... To find the sum, we should first determine the common difference and then use it to calculate each term up to the 5th one.

An arithmetic series is a sequence of numbers in which each term after the first is obtained by adding a constant, known as the common difference, to the previous term. For this series, we can identify the common difference by subtracting the first term from the second term:

18 - 8 = 10

Therefore, the common difference is 10.

Now we can find the first 5 terms of the series:

  • 1st term (a1) = 8
  • 2nd term (a2) = a1 + 10 = 18
  • 3rd term (a3) = a2 + 10 = 28
  • 4th term (a4) = a3 + 10 = 38
  • 5th term (a5) = a4 + 10 = 48

To find the sum of these terms, simply add them together:

8 + 18 + 28 + 38 + 48 = 140

The sum of the first 5 terms of the series is 140.

User Neil Fenwick
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