Arithmetic Sequence

• • Terms in Arithmetic Sequence:  Often, recognizing the pattern and finding the common difference is the challenge. Also, beware of the OBOE (Off By One Error) 

1985 AJHSME Problem 7

1988 AJHSME Problem 19

2022 AIME I Problem 6

2025 AMC 8 Problem 4

• • Sum of Arithmetic Sequence (Series)

1985 AJHSME Problem 2

1987 AJHSME Problem 3

1988 AJHSME Problem 4

1990 AJHSME Problem 11

1993 AJHSME Problem 19

1994 AJHSME Problem 2 Problem 17

2024 AMC 8 Problem 4

• • Simple "shortcuts": these facts can help you solve an arithmetic sequence problem much faster:

    • The average of an arithmetic sequence is simply its median

    • The average of an arithmetic sequence is also average of the highest and lowest term

1986 AJHSME Problem 25

2021 AIME II Problem 1

2023 AIME II Problem 1