WHICH TERM OF THE SEQUENCE 20,77/4, 37/2,71/4.......IS THE FIRST NEGATIVE TERM?

Dear Student,

20,, , 

2nd term - 1st term =  - 20 =  -  = .
3rd term - 2nd term =  -  =  -  = .
4th term - 3rd term =  -  =  -  = .
 
So the common difference is d = 

Use the nth term formula for an arithmetic sequence.

an = a1 + (n-1)d

1st term = a1 = 20, d = 

an = 20 + (n-1)

We set that < 0 to make it negative, and solve for n:

20 + (n-1) < 0

Multiply both sides by 4

80 + (n-1)(-3) < 0
80 + (-3)(n-1) < 0
   80 - 3(n-1) < 0
   80 - 3n + 3 < 0
       83 - 3n < 0
           -3n < -83
             n > 

So the 28th term is the first negative term.

That term is:

an = a1 + (n-1)d

a28 = 20 + (28-1)

a28 = 20 + (27)

a28 = 20 + 

a28 =  - 

a28 =