Find the sum 14+8+2+...+(−274)+(−280)

Given the arithmetic sequence:
14+8+2++(-274)+(-280)
Determine the sum.
Sum of Arithmetic sequence formula:
Sn =((a1+an)/2)n
Arithmetic sequence formula:
An=A1+(n-1)d
Solution:
1 st we must determine the common difference and number of terms. To find for the common difference,we subtract a2 by a1
Common difference: 8-14
Common difference: -6

Now we solve for the number of terms by using the formula for arithmetic sequence:
An=A1 +(n-1)-6
-280=14+(n-1)-6
-280=14-6n+6
-280=20-6n
-280-20=-6n
-300=-6n
n=40

Now we can solve for the sum of the arithmetic sequence.

Sn=((a1+an)/2)n
Sn=((14+ -280)/3)50
Sn= (-266/2)50
Sn=(-133)50
Sn= -6,650
Final
-6,650