Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence
-Find the sum of the first 50 terms of the arithmetic sequence: 5, -4, -13, -22, . . .
A)-10,775
B)-10,767
C)-445
D)-11,000

Question

Quizplus · Accepted Answer

We can use the formula for the sum of the first n terms of an arithmetic sequence: Sn = n/2(2a + (n-1)d), where Sn is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms. 
In this case, a = 5, d = -9 (since each term is decreasing by 9), and n = 50. Plugging these values into the formula, we get: 
S50 = 50/2(2(5) + (50-1)(-9)) 
= 25(10 - 441) 
= -10,775

Therefore, the best choice is A, which gives us the correct sum of the first 50 terms.

Use the Formula for the Sum of the First N