Find the term which doesn't fit into the series given below:

H4Q, K10N, N20K, Q43H, T90E

The correct option/answer is Q43H.

To find the term that does not fit into the series, we analyze the patterns of the first letter, the middle number, and the last letter of each term in the series: H4Q, K10N, N20K, Q43H, T90E.

1. Pattern of the First Letters:
Let us look at the alphabetical positions of the first letters of each term:
H = 8
K = 11
N = 14
Q = 17
T = 20
The difference between the alphabetical positions of any two consecutive first letters is constant:
$$11-8=3$$
$$14-11=3$$
$$17-14=3$$
$$20-17=3$$
Thus, the first letters follow a consistent pattern of adding 3 to their alphabetical values (+3).

2. Pattern of the Last Letters:
Let us look at the alphabetical positions of the last letters of each term:
Q = 17
N = 14
K = 11
H = 8
E = 5
The difference between the alphabetical positions of any two consecutive last letters is constant:
$$14-17=-3$$
$$11-14=-3$$
$$8-11=-3$$
$$5-8=-3$$
Thus, the last letters follow a consistent pattern of subtracting 3 from their alphabetical values (-3).

3. Pattern of the Numbers:
Let us analyze the sequence of the numbers in the terms: 4, 10, 20, 43, 90. Let us look at the differences between consecutive numbers:
$$d_1=10-4=6$$
$$d_2=20-10=10$$
If we look at the relation between these differences, we can establish an alternating progression where:
$$d_n=2\times d_{n-1}$$
where the constant $c_n$ alternates between −2 and +4.
Applying this rule to the differences:
First difference: $d_1=6$
Second difference:
$$d_2=2\times 6-2=10$$
Third difference (using +4 as the alternating constant):
$$d_3=2\times 10+4=24$$
Fourth difference (using −2 as the alternating constant):
$$d_4=2\times 24-2=46$$
Using this pattern, the numbers should be:
First number: 4
Second number: $4+6=10$
Third number: $10+10=20$
Fourth number:
$$20+24=44$$
Fifth number:
$$44+46=90$$
According to this established sequence, the fourth term in the series should contain the number 44 (which is Q44H). However, the given term contains the number 43 (Q43H), which makes Q43H the term that does not fit the series.