SOLUTION: in an arithmetic sequence, the sum of the first 20 terms is 950 and the sum of the second 20 terms is 0. find the general term of the sequence.

Sn = [2a1 + (n-1)d]

950 = [2a1 + (20-1)d] =

950 = 10[2a1 + 19d] =

Divide through by 10

95 = 2a1 + 19d

 
That means the sum of the first 40 terms is also 950

Sn = [2a1 + (n-1)d]

950 = [2a1 + (39)d] =

950 = 20[2a1 + 39d] =

Divide through by 10

95 = 2[2a1 + 39d]

95 = 4a1 + 78d

So we have this system of equations:

95 = 2a1 + 19d
95 = 4a1 + 78d

To eliminate a1, multiply the 
first one through by -2

-190 = -4a1 - 38d
  95 =  4a1 + 78d
-------------------
 -95 =  40d
  = d
  = d

95 = 2a1 + 19d
95 = 4a1 + 78d

To eliminate d, multiply the 
first one through by -78, and
the second one through by 19

-7410 = -156a1 - 1482d
 1805 =   76a1 + 1482d
-------------------
-5605 =  -80a1
 = a1
 = a1

Use nth term formula:

an = a1 + (n-1)d
an =  + (n-1)
an =  + (n-1)

Multiply through by 16

16an = 1121 + (-38)(n-1)

16an = 1121 - 38(n-1)

16an = 1121 - 38n + 1

16an = 1122 - 38n

Divide through by 2

8an = 561 - 19n

an = 

Edwin