Question

Find the sum of the first 25 terms of the arithmetic sequence given by the equation an = 6 - 3n

A. 275
B. 300
C. 325
D. 350

Answer 1

To find the sum of the first 25 terms of the arithmetic sequence given by the equation 6 - 3n, we can use the formula for the sum of an arithmetic series.

Step-by-step explanation:

To find the sum of the first 25 terms of the arithmetic sequence given by the equation an = 6 - 3n,

1. First, we need to find the value of the first term a1. Substitute n = 1 into the given equation: a1 = 6 - 3(1) = 3.
2. The common difference d can be found by subtracting the first term from the second term: d = a2 - a1 = (6 - 3(2)) - 3 = 0.
3. Using the formula for the sum of an arithmetic series: Sn = (n/2)(a1 + an), we can plug in the known values to calculate the sum: S25 = (25/2)(3 + (6 - 3(25))) = 25/2(3 - 72) = 25/2(-69) = -862.5.

Therefore, the sum of the first 25 terms of the arithmetic sequence is -862.5.