Over 7,039,000 live tutoring sessions served!
Geometric Sequences Worksheet
Practice Problems
[Given.]
Number of Princess each Queen had is 7 and so, the total number of Princess are 72.
Number of dolls each Princess had is 7 and so the total number of dolls = 73.
Number of dresses each doll had is 7 and so the total number of dresses = 74.
Number of diamond buttons each dress had is 7 and so the total number of diamond buttons = 75.
Number of Queens, number of Princess, number of dolls, number of doll's dresses, and the number of diamond buttons form a geometric sequence, 7, 72, 73, 74, 75.
Cost of each diamond button is $4900.
[Given.]
Total amount of all the diamond buttons = Total number of diamond bottuns × Cost of each diamond button.
= 75 × $4900.
[Substitute.]
= 16807 × 4900 = $82354300.
[Simplify.]
So, the total amount of all the diamond buttons is $82354300.
[Given.]
Number of Princess each Queen had is 7 and so, the total number of Princess are 72.
Number of rooms each Princess had is 7 and so the total number of rooms = 73.
Number of wall paintings each room had is 7 and so the total number of wall paintings = 74.
Number of Queens, number of princess, number of rooms and the number of paintings form a geometric sequence, 7, 72, 73, 74.
Cost of each painting is $400.
[Given.]
Total amount of all the paintings = Total number of paintings × Cost of each painting.
= 74 × $400.
[Substitute.]
= 2401 × 400 = $960400.
[Simplify.]
So, the total amount of all the paintings is $960400.
Geometric Sequences Worksheet
- Page 1
1.
There lived a King who had 7 Queens. Each Queen had 7 Princess, each Princess had 7 dolls, each doll had 7 dresses and each dress had 7 daimond buttons. If the cost of each button is $4900, then find the total cost of all the diamond buttons.
| a. | $82354200 | ||
| b. | $82354500 | ||
| c. | $82354400 | ||
 | d. | $82354300 |
Solution:
Number of Queens the King had is 7.[Given.]
Number of Princess each Queen had is 7 and so, the total number of Princess are 72.
Number of dolls each Princess had is 7 and so the total number of dolls = 73.
Number of dresses each doll had is 7 and so the total number of dresses = 74.
Number of diamond buttons each dress had is 7 and so the total number of diamond buttons = 75.
Number of Queens, number of Princess, number of dolls, number of doll's dresses, and the number of diamond buttons form a geometric sequence, 7, 72, 73, 74, 75.
Cost of each diamond button is $4900.
[Given.]
Total amount of all the diamond buttons = Total number of diamond bottuns × Cost of each diamond button.
= 75 × $4900.
[Substitute.]
= 16807 × 4900 = $82354300.
[Simplify.]
So, the total amount of all the diamond buttons is $82354300.
Correct answer : (4)
2.
Once upon a time there lived a King who had 7 Queens. Each Queen had 7 Princess, each Princess had 7 rooms, each room had 7 wall paintings. If the cost of each painting is $400, then find the total amount of all the paintings.
| a. | $960400 | |
| b. | $960500 | ||
| c. | $960300 | ||
| d. | $960600 |
Solution:
Number of Queens the King had is 7.[Given.]
Number of Princess each Queen had is 7 and so, the total number of Princess are 72.
Number of rooms each Princess had is 7 and so the total number of rooms = 73.
Number of wall paintings each room had is 7 and so the total number of wall paintings = 74.
Number of Queens, number of princess, number of rooms and the number of paintings form a geometric sequence, 7, 72, 73, 74.
Cost of each painting is $400.
[Given.]
Total amount of all the paintings = Total number of paintings × Cost of each painting.
= 74 × $400.
[Substitute.]
= 2401 × 400 = $960400.
[Simplify.]
So, the total amount of all the paintings is $960400.
Correct answer : (1)
3.
What would be the next three terms in order of the geometric series?
2, 8, 32, 128, . . . .
| a. | 512, 2048, and 6144 | ||
| b. | 8192, 2048, and 512 | ||
| c. | 512, 2048, and 8192 | |
| d. | 512, 8192, and 2048 |
Answer: (c)
Correct answer : (3)
4.
What would be the seventh term of the geometric sequence?
3, 9, 27, 81, . . . .
| a. | 6561 | ||
| b. | 243 | ||
| c. | 2187 | |
| d. | 729 |
Answer: (c)
Correct answer : (3)
5.
Find the next term in the sequence:
6, 48, 384, 3072, ...
6, 48, 384, 3072, ...
| a. | 24574 | ||
| b. | 24576 | |
| c. | 24572 | ||
| d. | 24578 |
Answer: (b)
Correct answer : (2)
6.
Find the smallest of three geometric means between 7 and 4375.
| a. | 875 | ||
| b. | 175 | ||
| c. | 105 | ||
| d. | 35 |
Answer: (d)
Correct answer : (4)
7.
Find the geometric mean of the numbers 2 and 10.
| a. | 2 | |
| b. | 4 | ||
| c. | 5 | ||
| d. | 4 |
Answer: (a)
Correct answer : (1)
8.
The geometric mean of numbers and 14 is 7. Find .
| a. | 98 | ||
| b. | |||
| c. | 7 | |
| d. | 9 |
Answer: (c)
Correct answer : (3)
9.
The sequence 3, 6, 12, 24... falls under which of the following categories?
| a. | Arithmetic | ||
| b. | Geometric | |
| c. | Both | ||
| d. | Neither |
Answer: (b)
Correct answer : (2)
10.
Evaluate the expression 5 × 4 for = 1, 2, 3 and 4 and identify the sequence formed.
| a. | Geometric | |
| b. | Arithmetic | ||
| c. | Both | ||
| d. | Neither |
Answer: (a)
Correct answer : (1)