Find the sum, of the sequence.
--1, -5, -9, -13, . . ., -77
A) -770
B) -820
C) -780
D) -81

Question

Find the sum,  of the sequence.
--1, -5, -9, -13, . . ., -77
A) -770 
B) -820 
C) -780 
D) -81

Quizplus · Accepted Answer

The given sequence is an arithmetic sequence with a common difference of -4. Therefore, we can use the formula for the sum of an arithmetic sequence: 
sum = (number of terms)*(average of first and last term)
To find the number of terms, we can use the formula:
last term = first term + (number of terms - 1)*common difference
-77 = -1 + (number of terms - 1)*(-4)
Number of terms = 20
Now, we can find the average of the first and last terms:
average = (-1 - 77)/2 = -39
Finally, we can find the sum:
sum = 20*(-39) = -780
Therefore, the answer is C. To find the sum of an arithmetic sequence, we can use the formula:
Sn = n/2(2a + (n-1)d)
where
Sn = sum of the first n terms of the sequence
n = number of terms in the sequence
a = first term
d = common difference

In this case,
a = -1 (first term)
d = -4 (common difference)
We need to find n, the number of terms. We can use the formula for the nth term of an arithmetic sequence:
an = a + (n-1)d
-77 = -1 + (n-1)(-4)
-77 = -1 - 4n + 4
-80 = -4n
n = 20

Now we can substitute into the formula for the sum:
Sn = n/2(2a + (n-1)d)
Sn = 20/2(-2 + (19)(-4))
Sn = 10(-2 - 76)
Sn = -780

Therefore, the answer is C, -780.

Find the Sum, of the Sequence