The first two terms of a sequence are 4 and 12. If the sequence is arithmetic, what is the next term? If the sequence is geometric, what is the next term?

Step-by-step explanation:

Case 1:  20; Case 2:  36

Case 1:  arithmetic sequence

The common difference is 8.  Notice that 4 + 8 = 12.

a(1) = 4; a(2) = 12; a(3) = 20; etc.

The common next term (3rd term) is 20.

Case 2:  geometric sequence

The common ratio is 3.  Notice that 4*3 = 12.

Multiplying this second term by the common ratio (3) results in the third term:  36.

5

step-by-step explanation:

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal