We need to complete the given letter-number series for questions 18, 19, 20, and 21.

Discrete MathematicsSequencesSeriesPattern RecognitionLetter-Number Series
2025/4/16

1. Problem Description

We need to complete the given letter-number series for questions 18, 19, 20, and
2
1.

2. Solution Steps

* Problem 18: AB50, DE49, GH48, JK47, \_\_\_, \_\_\_
* Letters: The first letters are A, D, G, J. The differences in position in the alphabet are DA=3D-A = 3, GD=3G-D=3, JG=3J-G=3. So the next letters should be J+3=MJ+3=M and M+3=PM+3=P. The second letters are B, E, H, K. The differences are EB=3E-B=3, HE=3H-E=3, KH=3K-H=3. So the next letters should be K+3=NK+3=N and N+3=QN+3=Q.
* Numbers: The numbers are 50, 49, 48,
4

7. So the next numbers should be 46 and

4

5. * Therefore, the next two terms in the series are MN46 and PQ

4
5.
* Problem 19: Z100, Y200, X300, W400, \_\_\_, \_\_\_
* Letters: The letters are Z, Y, X, W. The positions are decreasing by 1 each time. So the next letters should be V and U.
* Numbers: The numbers are 100, 200, 300,
4
0

0. The numbers are increasing by 100 each time. So the next numbers should be 500 and

6
0

0. * Therefore, the next two terms in the series are V500 and U

6
0
0.
* Problem 20: PQ46, RS55, TU64, \_\_\_, \_\_\_
* Letters: The first letters are P, R, T. The differences in position in the alphabet are RP=2R-P = 2, TR=2T-R=2. So the next letters should be T+2=VT+2=V and V+2=XV+2=X. The second letters are Q, S, U. The differences are SQ=2S-Q=2, US=2U-S=2. So the next letters should be U+2=WU+2=W and W+2=YW+2=Y.
* Numbers: The numbers are 46, 55,
6

4. The differences are $55-46=9$ and $64-55=9$. So the next numbers should be $64+9=73$ and $73+9=82$.

* Therefore, the next two terms in the series are VW73 and XY
8
2.
* Problem 21: H18I, G17H, F16G, \_\_\_
* Letters: The first letters are H, G, F. The letters are decreasing by 1 each time. So the next letter should be E.
* Numbers: The numbers are 18, 17,
1

6. The numbers are decreasing by 1 each time. So the next number should be

1

5. * The third letters are I, H, G. The letters are decreasing by 1 each time. So the next letter should be F.

* Therefore, the next term in the series is E15F.

3. Final Answer

* Problem 18: MN46, PQ45
* Problem 19: V500, U600
* Problem 20: VW73, XY82
* Problem 21: E15F

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