Correct Answer – Option 4 : monotonic

Concept:

 A sequence {a_n} is said to be 

• increasing if m < n implies a_m ≤ a_n
• strictly increasing if m < n implies am < an 
• decreasing if m < n implies  a_m ≥ a_n
• strictly decreasing if m < n implies am > an 
• monotone if it is either increasing or decreasing

Calculation:

 Let us look at the first few terms of this sequence. These are 

3, 9/2, 9/2, 27/8, 81/80, 243/560, ….

You can see that the first 5 terms of this sequence are in increasing order However, the 6^th term is less than the 5^th term. Hence, the sequence is neither increasing nor decreasing. That is the sequence is not monotone.