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 | seats | running total)

   1 | 12 | 12; 2 | 14 | 26; 3 | 16 | 42; the rows go on, + 2 on each arrow.

2. 1.

   Ari adds up the seats in a hall, row by row. Each row has 2 more seats than the row before. What is the running total after row 6?

   102

3. Growth table (row | cans | running total)

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

4. 2.

   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

5. Growth table (week | dollars | running total)

   1 | 10 | 10; 2 | 15 | 25; 3 | 20 | 45; the rows go on, + 5 on each arrow.

6. 3.

   Esme's parents add $5 more to a savings fund each week than the week before. How many dollars are in the fund after week 6?

   135

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

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

8. 4.

   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
9. 5.

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

   210
10. 6.

    Pia expands Σ from k = 1 to 5 of (2k + 3) on the class board. The expanded row starts with 5 and 7. What is the sum?

    45
11. 7.

    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
12. 8.

    Zee expands Σ from k = 2 to 6 of (5k − 2) on the class board. The expanded row starts with 8 and 13. What is the sum?

    90
13. 9.

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

    20
14. 10.

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

    21