Explanation:

- The words in the options are given to identify the one with incorrect spelling.

- Option 1: architecture - This word is correctly spelled. It refers to the art or practice of designing and constructing buildings.

- Option 2: appropriate - This word is also correctly spelled. It means suitable or proper in the circumstances.

- Option 3: appreciation - This word is written correctly. It means the recognition and enjoyment of the good qualities of someone or something.

- Option 4: arithmatic - This is the incorrectly spelt word. The correct spelling is "arithmetic," which refers to the branch of mathematics dealing with numbers and basic operations.

The incorrect spelling is in Option 4: arithmatic