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There are 8 varieties of monkey in a certain zoo . The number of each variety forms a G.P . If the 4th and 6th variety consist of 54 and 486 monkeys respectively, find the number in the first and last variety?
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There are 8 varieties of monkey in a certain zoo . The number of each ...
Problem Statement:
There are 8 varieties of monkeys in a certain zoo, and the number of monkeys in each variety forms a geometric progression (G.P). Given that the 4th and 6th varieties consist of 54 and 486 monkeys respectively, we need to find the number of monkeys in the first and last varieties.
Solution:
Let's denote the number of monkeys in the first variety as 'a' and the common ratio between the varieties as 'r'. Since the number of monkeys forms a geometric progression, we can write the following equations:
For the 4th variety:
a * r^3 = 54 ...(1)
For the 6th variety:
a * r^5 = 486 ...(2)
We can solve these equations to find the values of 'a' and 'r'.
Solving Equation (1):
Divide Equation (2) by Equation (1) to eliminate 'a':
(a * r^5) / (a * r^3) = 486 / 54
r^2 = 9
Taking the square root of both sides:
r = 3
Solving Equation (1) with 'r = 3':
Substituting the value of 'r' into Equation (1):
a * 3^3 = 54
27a = 54
a = 2
Therefore, the number of monkeys in the first variety is 2.
Calculating the last variety:
To find the number of monkeys in the last variety, we need to calculate the 8th term of the geometric progression.
Using the formula for the nth term of a geometric progression:
nth term = a * r^(n-1)
Plugging in the values:
8th term = 2 * 3^(8-1)
8th term = 2 * 3^7
8th term = 2 * 2187
8th term = 4374
Therefore, the number of monkeys in the last variety is 4374.
Summary:
- The number of monkeys in each variety forms a geometric progression.
- By solving the given equations, we found that the number of monkeys in the first variety is 2 and in the last variety is 4374.
There are 8 varieties of monkeys in a certain zoo, and the number of monkeys in each variety forms a geometric progression (G.P). Given that the 4th and 6th varieties consist of 54 and 486 monkeys respectively, we need to find the number of monkeys in the first and last varieties.
Solution:
Let's denote the number of monkeys in the first variety as 'a' and the common ratio between the varieties as 'r'. Since the number of monkeys forms a geometric progression, we can write the following equations:
For the 4th variety:
a * r^3 = 54 ...(1)
For the 6th variety:
a * r^5 = 486 ...(2)
We can solve these equations to find the values of 'a' and 'r'.
Solving Equation (1):
Divide Equation (2) by Equation (1) to eliminate 'a':
(a * r^5) / (a * r^3) = 486 / 54
r^2 = 9
Taking the square root of both sides:
r = 3
Solving Equation (1) with 'r = 3':
Substituting the value of 'r' into Equation (1):
a * 3^3 = 54
27a = 54
a = 2
Therefore, the number of monkeys in the first variety is 2.
Calculating the last variety:
To find the number of monkeys in the last variety, we need to calculate the 8th term of the geometric progression.
Using the formula for the nth term of a geometric progression:
nth term = a * r^(n-1)
Plugging in the values:
8th term = 2 * 3^(8-1)
8th term = 2 * 3^7
8th term = 2 * 2187
8th term = 4374
Therefore, the number of monkeys in the last variety is 4374.
Summary:
- The number of monkeys in each variety forms a geometric progression.
- By solving the given equations, we found that the number of monkeys in the first variety is 2 and in the last variety is 4374.
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There are 8 varieties of monkey in a certain zoo . The number of each variety forms a G.P . If the 4th and 6th variety consist of 54 and 486 monkeys respectively, find the number in the first and last variety?
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There are 8 varieties of monkey in a certain zoo . The number of each variety forms a G.P . If the 4th and 6th variety consist of 54 and 486 monkeys respectively, find the number in the first and last variety? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about There are 8 varieties of monkey in a certain zoo . The number of each variety forms a G.P . If the 4th and 6th variety consist of 54 and 486 monkeys respectively, find the number in the first and last variety? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 8 varieties of monkey in a certain zoo . The number of each variety forms a G.P . If the 4th and 6th variety consist of 54 and 486 monkeys respectively, find the number in the first and last variety?.
There are 8 varieties of monkey in a certain zoo . The number of each variety forms a G.P . If the 4th and 6th variety consist of 54 and 486 monkeys respectively, find the number in the first and last variety? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about There are 8 varieties of monkey in a certain zoo . The number of each variety forms a G.P . If the 4th and 6th variety consist of 54 and 486 monkeys respectively, find the number in the first and last variety? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 8 varieties of monkey in a certain zoo . The number of each variety forms a G.P . If the 4th and 6th variety consist of 54 and 486 monkeys respectively, find the number in the first and last variety?.
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