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

Answer 1

A1 = 100

A4 = 76

Ak = A1 + D * (k-1) where D is the common difference

A2 = A1 + D = 100 + D

A3 = A1 + 2 * D = 100 + 2D

76 = A4 = A1 + 3*D = 100 + 3D

76 = 100 + 3D

-24 = 3D

D = -8

the common difference is -8

using the formula again:

100 + (-8)*k < 0

(-8)*k < -100

8k > 100

k>100/8 = 50/4 = 25/2 = 12.5

so it will take 13 more terms for the sequence to go negative.

That makes it the 14th term....

the sequence is 100, 92, 84, 76, 68, 60, 52, 44, 36, 28, 20, 12, 4, -4

14th term