Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A pattern of tiles starts with 3 tiles in the first row, and each subsequent row has 2 more tiles than the previous row. If there are 10 rows of tiles, how many tiles are in the 10th row?
- A25 tiles
- B21 tiles
- C23 tiles
- D19 tiles
Show answer & explanationAnswer & explanation
Correct answer: B. 21 tiles
This is an arithmetic sequence. The first term (a_1) is 3, and the common difference (d) is 2. We need to find the 10th term (a_10) using the formula a_n = a_1 + (n-1)d. So, a_10 = 3 + (10-1)2 = 3 + 9*2 = 3 + 18 = 21.
Why the other options are wrong
- A. Incorrect. This is too high and indicates a significant miscalculation.
- C. Incorrect. This is a plausible distractor resulting from a small arithmetic error.
- D. Incorrect. This might be from a calculation error, perhaps using n instead of (n-1).
Arithmetic Sequence Nth Term
The formula a_n = a_1 + (n-1)d allows you to calculate any term (a_n) in an arithmetic sequence given the first term (a_1), the term number (n), and the common difference (d).
- a_1 is the first term.
- d is the common difference (each term is d more/less than the previous).
- n is the position of the term you want to find.
- The (n-1) factor accounts for the number of 'steps' from the first term.
Memory trick: Starting point plus steps times difference, that's the nth term's essence.