The sum of the finite arithmetic series can be calculated using the formula:
S = n/2 * (a + l)
- S = sum of the series
- n = number of terms
- a = first term
- l = last term
In this series, the first term a is 26, and the last term l is 44. To find the number of terms n, we can observe that this series increases by a common difference of 3.
The terms are:
- 26
- 29
- 32
- 35
- 38
- 41
- 44
Counting these, we find there are 7 terms. Now, we can plug in the values into the formula:
S = 7/2 * (26 + 44)
First, calculate the sum inside the parentheses:
26 + 44 = 70
Now, substitute this back into the sum formula:
S = 7/2 * 70
This simplifies to:
S = 7 * 35 = 245
Therefore, the sum of the finite arithmetic series 26, 29, 32, 35, 38, 41, 44 is 245.