In an arithmetic sequence, the first term is 100 and the fourth term is 76. What is the value of the first term that is less than 0?

We can find the common difference as

76  -100          -  24

_______  =       ___    =   -  8

     3                   3

So  we need to solve this

100 -  8(n - 1)  =  0

100 - 8n + 8  =0

108  - 8n  = 0

54 - 4n  =  0

54  = 4n

54/4   = n

27/2  = n

13.5  = n

The  14th term will be < 0   ......so

100 - 8 (14 - 1)  =

100 - 8 * 13  =

100 - 104   =

-4