Sum of a finite geometric series, and infinite geometric series

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Bo works out 5 + 15 + 45 + … + 1215 on a math club card. What is the sum?

   1820
2. 2.

   Esme works out 486 + 162 + 54 + … + 2 on a math club card. What is the sum?

   728
3. 3.

   Jun works out 1024 + 256 + 64 + … + 1 on a math club card. What is the sum?

   1365
4. 4.

   Noah writes the infinite series 36 − 24 + 16 − … on the class board. What number does its running total approach?

   108/5
5. 5.

   Pia's grandparents add $200 to a savings fund at the end of each year, and it grows 4% a year. To the nearest cent, what does it hold right after deposit 5?

   $1,083.26
6. 6.

   Ren's parents add $500 to a savings fund at the end of each year, and it grows 3% a year. To the nearest cent, what does it hold right after deposit 6?

   $3,234.20
7. 7.

   Zee's parents add $250 to a savings fund at the end of each year, and it grows 2% a year. To the nearest cent, what does it hold right after deposit 8?

   $2,145.74
8. 8.

   Ari writes the infinite series 32 + 24 + 18 + … on the class board. Which statement about its total is right?

   • Total 128, since 32 ÷ (1 − 3/4) = 128
   • Total 74, the sum of the terms shown
   • No total, since the terms never reach 0
   • Total 128/3, since 32 ÷ (3/4) = 128/3
9. 9.

   Bo writes the infinite series 27 − 9 + 3 − … on the class board. Which statement about its total is right?

   • Total -81, since 27 ÷ (-1/3) = -81
   • Total 20.25, since 27 ÷ (1 − (-1/3)) = 20.25
   • No total, since the terms never reach 0 and keep going
   • Total 21, the sum of the terms shown
10. 10.

    Jun writes the infinite series 8 − 12 + 18 − … on the class board. Which statement about its total is right?

    • Total 14, the sum of the terms shown
    • No total, since r = -3/2 and the total swings further each time
    • Total -16/3, since 8 ÷ (-3/2) = -16/3
    • Total 3.2, since 8 ÷ (1 − (-3/2)) = 3.2