We are given a series:
\[
G4T, J10R, M20P, P43N, S90L, V185J.
\]
Let’s break down each term into three parts: a letter, a number, and another letter.
1. First Letter Pattern:
G, J, M, P, S, V.
These are letters with a common difference of 3 in their positions in the alphabet:
\[
G (7), J (10), M (13), P (16), S (19), V (22).
\]
The sequence of letters is increasing by 3 positions each time.
2. Middle Number Pattern:
4, 10, 20, 43, 90, 185.
The pattern of these numbers is not immediately obvious, but by examining the differences:
\[
10 - 4 = 6, \quad 20 - 10 = 10, \quad 43 - 20 = 23, \quad 90 - 43 = 47, \quad 185 - 90 = 95.
\]
The differences between consecutive numbers are increasing by a factor of approximately 2.
3. Third Letter Pattern:
T, R, P, N, L, J.
These letters are decreasing by a step of 2 positions in the alphabet:
\[
T (20), R (18), P (16), N (14), L (12), J (10).
\]
The sequence of letters is decreasing by 2 positions each time.
Now, let’s check the sequence J10R:
- The first letter J (10) fits with the letter sequence.
- The number 10 does not follow the expected pattern, as the difference from the previous term (G4T) should have been a more significant number according to the pattern we established.
- The third letter R (18) also fits the decreasing letter pattern.
However, due to the number 10 not fitting the progression of numbers in the sequence, the odd term is J10R.