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.

   Ari works out 3 + 6 + 12 + … + 384 on a math club card. What is the sum?

   765
2. 2.

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

   1820
3. 3.

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

   728
4. 4.

   Kira writes the infinite series 27 + 9 + 3 + … on the class board. What number does its running total approach?

   81/2
5. 5.

   Luz writes the infinite series 48 + 12 + 3 + … on the class board. What number does its running total approach?

   64
6. 6.

   Milo writes the infinite series 20 − 10 + 5 − … on the class board. What number does its running total approach?

   40/3
7. 7.

   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
8. 8.

   Tala's grandparents add $100 to a savings fund at the end of each year, and it grows 5% a year. To the nearest cent, what does it hold right after deposit 10?

   $1,257.79
9. 9.

   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 128/3, since 32 ÷ (3/4) = 128/3
   • Total 74, the sum of the terms shown
   • No total, since the terms never reach 0
10. 10.

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

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