Series and sigma notation, and the sum of an arithmetic series

Answer Key - Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. Read this first

   Growth table (row | cans | running total)

   1 | 2 | 2; 2 | 3 | 5; 3 | 4 | 9; the rows go on, + 1 on each arrow.

2. 1.

   Bo stacks cans in rows, and each row down has 1 more can than the row above. How many cans are in the top 7 rows together?

   35

3. Growth table (step | blocks | running total)

   1 | 3 | 3; 2 | 6 | 9; 3 | 9 | 18; the rows go on, + 3 on each arrow.

4. 2.

   Jun builds a staircase model, and each step uses 3 more blocks than the step before. How many blocks do steps 1 to 5 use in all?

   45
5. 3.

   Kira pairs the 10 terms of 3 + 7 + 11 + … + 39 from both ends, and each pair adds to 42. What is the sum?

   210
6. 4.

   Noah pairs the 11 terms of 2 + 5 + 8 + … + 32 from both ends, and each pair adds to 34. What is the sum?

   187
7. 5.

   Ren expands Σ from k = 1 to 6 of (3k − 1) on the class board. The expanded row starts with 2 and 5. What is the sum?

   57
8. 6.

   Tala expands Σ from k = 0 to 5 of (4k + 1) on the class board. The expanded row starts with 1 and 5. What is the sum?

   66
9. 7.

   Ari counts the terms of Σ from k = 4 to 15 of (2k − 1). How many terms are there?

   12
10. 8.

    Bo counts the terms of Σ from k = 3 to 20 of (3k + 1). How many terms are there?

    18
11. 9.

    Esme counts the terms of 7 + 11 + 15 + … + 83. How many terms are there?

    20
12. 10.

    Jun counts the terms of 5 + 8 + 11 + … + 65. How many terms are there?

    21