Find the next term in the alpha-numeric series D4T, F9R, H20P, J43N.

The correct option is L90L.

To find the next term in the alpha-numeric series D4T, F9R, H20P, J43N, we analyze the patterns of the first letter, the middle number, and the last letter of each term separately.

1. Pattern of the First Letter:
The first letters of the terms are D, F, H, and J.
Let us look at their alphabetical positions:
D is the 4th letter.
F is the 6th letter (4 + 2).
H is the 8th letter (6 + 2).
J is the 10th letter (8 + 2).
Following this pattern of adding 2 to the position, the next first letter must be the 12th letter of the alphabet, which is L.

2. Pattern of the Middle Number:
The numbers are 4, 9, 20, and 43.
Let's find the relation between consecutive numbers:
$(4\times 2)+1=9$
$(9\times 2)+2=20$
$(20\times 2)+3=43$
The pattern is to multiply the previous term by 2 and add an increasing integer (+1, +2, +3, ...).
Following this rule, the next number is:
$(43\times 2)+4=86+4=90$

3. Pattern of the Last Letter:
The last letters of the terms are T, R, P, and N.
Let us look at their alphabetical positions in reverse order:
T is the 20th letter.
R is the 18th letter (20 - 2).
P is the 16th letter (18 - 2).
N is the 14th letter (16 - 2).
Following this pattern of subtracting 2 from the position, the next last letter must be the 12th letter of the alphabet, which is L.

Combining the three parts (First Letter = L, Middle Number = 90, Last Letter = L), we get the next term in the series as L90L.