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.