Arithmetic Sequences Worksheets Grade 12

1. Noah is arranging square tiles in a visual pyramid pattern. The bottom row has 21 tiles, the next row up has 16 tiles, and each subsequent row has 5 fewer tiles than the row below it, forming an arithmetic sequence. How many tiles are in the 6th row from the bottom? What is the total number of tiles in the entire pyramid if it continues until the top row has 1 tile?
2. Sequence: 14, 23, 32, 41... Find a₁₈ and sum of first 18 terms.
3. Olivia is a financial analyst for a growing startup. The company's monthly profit (in thousands of dollars) follows an arithmetic sequence. In the first month (n=1), the profit was $5,000. The common difference in monthly profit is an increase of $3,000. What is the total profit, in thousands of dollars, that the company earned from the first month through the 20th month?

…and 3 more problems

1. Emma is training for a charity run and is increasing her weekly running distance by a constant amount each week. In week 1, she runs 7 km. In week 7, she runs 43 km. Her goal is to run at least 100 km in a single week. Assuming the pattern continues, what is the minimum number of weeks she needs to train to reach or exceed 100 km in a week, and what is her total running distance over all those weeks from week 1 up to and including that week?
2. Mere is constructing a visual pyramid of square tiles. The bottom row has 2 tiles. The second row from the bottom has 4 tiles, the third row from the bottom has 6 tiles, and so on, with each row above having 2 more tiles than the row below it, forming an arithmetic sequence. There are 12 rows in total. What is the total number of tiles in the pyramid?
3. A geometric pattern is formed by stacking triangular layers of blocks. The first layer has 1 block, the second layer has 3 blocks arranged in a triangle, the third layer has 6 blocks in a larger triangle, and this pattern continues where each subsequent layer forms a triangular number pattern (1, 3, 6, 10, 15...). If the pattern has n layers, the total number of blocks is given by the sum of the first n triangular numbers. Find the explicit formula for the total number of blocks in terms of n.

…and 4 more problems

1. Matiu is creating a visual art piece using square tiles arranged in concentric square rings. The innermost ring (Ring 1) has 4 tiles (one on each side of a 2×2 square). Ring 2 has 12 tiles forming the next square border around Ring 1. Ring 3 has 20 tiles, and so on, forming an arithmetic sequence of the number of tiles in each ring. If Matiu continues this pattern until he has 10 complete rings, what is the total number of tiles used in the entire artwork?
2. A geometric pattern is formed by stacking triangular layers. The first layer has 1 equilateral triangle with side length 2 cm. The second layer has 3 equilateral triangles, each with side length 1 cm, arranged to form a larger triangle. The third layer has 5 equilateral triangles, each with side length 0.5 cm, continuing this pattern. If the pattern continues infinitely with each subsequent layer having 2 more triangles than the previous layer and each triangle having half the side length of the triangles in the previous layer, what is the total area of all triangles in this infinite series? (Area of equilateral triangle = (√3/4) × side²)
3. Sequence: 9, 17, 25, 33... Find a₁₄ and sum of first 14 terms.

…and 3 more problems