To find the sum of the first 21 terms of the arithmetic series defined by the sequence 5, 3, 1, 1, we first need to identify the common difference.
The common difference (d) can be found by subtracting the first term from the second:
d = 3 – 5 = -2
However, to properly analyze the series further, let’s observe that after the first two terms, the series becomes constant (1). Thus, the terms can be simplified as follows:
- 1st term: 5
- 2nd term: 3
- 3rd term: 1
- 4th term: 1 (and all subsequent terms)
Now, let’s outline the terms based on this understanding:
- 1st term: 5
- 2nd term: 3
- 3rd term: 1
- 4th term to 21st term: 1 (18 times)
To find the sum, we add these values together:
Sum = 5 + 3 + 1 + (1 * 18)
Calculating this gives us:
Sum = 5 + 3 + 1 + 18 = 27
Therefore, the sum of the first 21 terms of the arithmetic series is 27.