To find the sum of a finite arithmetic series, you can follow a systematic approach. The series presented is:
26, 29, 32, 35, 38, 41, 44.
This series has the following characteristics:
- First term (a): The first term of the series is 26.
- Common difference (d): The common difference can be found by subtracting the first term from the second term: 29 – 26 = 3.
- Last term (l): The last term of the series is 44.
- Number of terms (n): To find the number of terms, we can use the formula for the n-th term of an arithmetic sequence: l = a + (n – 1) * d. Setting l to 44:
44 = 26 + (n – 1) * 3
44 – 26 = (n – 1) * 3
18 = (n – 1) * 3
n – 1 = 6
n = 7
So, there are 7 terms in this series.
Now that we have the necessary values, we can use the formula for the sum of an arithmetic series:
Sum (S) = n/2 * (a + l)
Substituting the values we found:
S = 7/2 * (26 + 44)
= 7/2 * 70
= 7 * 35
= 245
Therefore, the sum of the finite arithmetic series is 245.