56.2k views
1 vote
Find the sum of the first 5 terms of the infinite series 8 + 18 + 28 + ...

User RobertT
by
8.7k points

1 Answer

2 votes

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
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories