1) If the number 1,1/3,1/9, are terms of Geometric progression. Find its common ratio
2) If the second term of Geometric progression is equal to 3, and the 5th term is equal to 81/8. Find the 7th term.
3)If x,y,3 is a Geometric progression. Find the value of x and y
4) Insert 4 numbers between 128 and 4 to form a Geometric progression
5) The average maximum temperature in Cairo town in 1999 was 40 degree C in June, 30 degree C in July, 25.6 degree C in August and it is continue to decrease in the same manner during the following months. what will the average maximum temperature of Cairo be in February 2000 AD {(0.8)to the power of eight 0.168)
1.
r = 2nd/1st or 3rd/2nd
= (1/3) / 1 or (1/9) / (1/3)
= 1/3 for both
2.
ar = 3
ar^4 = 81/8
divide the second equation by the first
r^3 = 27/8
r = 3/2
take it from there
3. to be a GS
y/x = 3/y
y^2 = 3x
that's all you can do, unless you know either x or y
4.
128 , 128r , 128r^2 , 128r^3 , 128r^4 , 4
then 128r/128 = 4/(128r^4)
solve for r
5. you try it, it's easy.
giyfif
The numbers 27;x;y are in geometric progression if the sum of these numbers is 21 calculate the possible value of x and y
1) To find the common ratio, we need to determine the ratio between any two consecutive terms. In this case, let's find the ratio between the second term (1/3) and the first term (1).
The common ratio (r) is found by dividing the second term by the first term:
r = 1/3 / 1 = 1/3.
Therefore, the common ratio of the geometric progression is 1/3.
2) To find the 7th term of a geometric progression, we need to know the common ratio and either the second term or the first term. In this case, we have the second term and the 5th term.
Given:
Second term (a2) = 3
Fifth term (a5) = 81/8
We can use these values to find the common ratio (r). The formula for finding the nth term of a geometric progression is:
an = a1 * r^(n-1),
where a1 is the first term, r is the common ratio, and n is the term number.
Using the values provided, we can set up two equations:
a2 = a1 * r^(2-1) --> 3 = a1 * r
a5 = a1 * r^(5-1) --> 81/8 = a1 * r^4
From the first equation, we can express a1 in terms of r:
a1 = 3/r.
Substituting this value into the second equation:
81/8 = (3/r) * r^4.
Simplifying the equation:
81/8 = 3r^3.
Multiplying both sides by 8 to get rid of the fraction:
81 = 24r^3.
Dividing both sides by 24 to isolate r^3:
r^3 = 81/24.
Taking the cube root of both sides to solve for r:
r = (81/24)^(1/3) = 3^(1/3) = 3^(1/3) * 2/2 = (3 * 2)^(1/3) * 2^(1/3) = 6^(1/3) * 2^(1/3) = 2 * 6^(1/3).
Now that we have the value of r, we can find the 7th term (a7) using the formula mentioned earlier:
a7 = a1 * r^(7-1) --> a7 = (3/r) * r^6 = 3 * r^5.
Substituting the value of r we found:
a7 = 3 * (2 * 6^(1/3))^5.
Simplifying the expression:
a7 = 3 * 2^5 * 6^(5/3).
Therefore, the 7th term of the geometric progression is 3 * 2^5 * 6^(5/3).
3) To find the values of x and y in the geometric progression x, y, 3, we need to determine the common ratio. We know that each term is obtained by multiplying the previous term by the common ratio.
So, we can write the following equations:
y = x * r
3 = y * r
To solve these equations, we can substitute the value of y from the first equation into the second equation:
3 = (x * r) * r
3 = x * r^2
Now, we can solve for x by isolating it in terms of r:
x = 3 / r^2
Substituting this value back into the first equation, we can solve for y:
y = x * r
y = (3 / r^2) * r
y = 3 / r
So, the value of x is 3 / r^2 and the value of y is 3 / r in the geometric progression x, y, 3.
4) To insert 4 numbers between 128 and 4 to form a geometric progression, we need to determine the common ratio.
Let's call the 4 numbers to be inserted as a1, a2, a3, and a4.
Given:
First term (a) = 128
Last term (an) = 4
Number of terms (n) = 6 (including the inserted numbers)
Using the formula for the nth term of a geometric progression:
an = a * r^(n-1)
We can set up two equations:
4 = 128 * r^(6-1)
4 = 128 * r^5
Dividing both sides by 128:
4/128 = r^5
Taking the 5th root of both sides to solve for r:
r = (4/128)^(1/5) = 2/4 = 1/2
Now that we have the value of r, we can use it to find the common ratio between the inserted numbers:
The common ratio (r) is (1/2).
To find the values of the 4 inserted numbers, we can multiply the previous number by the common ratio:
a1 = 128 * (1/2)
a2 = a1 * (1/2)
a3 = a2 * (1/2)
a4 = a3 * (1/2)
Therefore, the 4 numbers between 128 and 4 in the geometric progression are: 64, 32, 16, and 8.
5) To find the average maximum temperature of Cairo in February 2000 AD, given that the temperature decreases in a specific manner, we need to determine the pattern.
Given:
Average maximum temperature in June 1999 = 40 degrees C
Average maximum temperature in July 1999 = 30 degrees C
Average maximum temperature in August 1999 = 25.6 degrees C
We can observe that the temperature is decreasing each month by multiplying with a certain factor, which is stated as (0.8)^8.
To find the average maximum temperature in February 2000 AD, we need to multiply the August temperature by this factor. Let's calculate it:
Temperature in February 2000 AD = August 1999 temperature * (0.8)^8
Temperature in February 2000 AD = 25.6 * (0.8)^8
Evaluating the expression:
Temperature in February 2000 AD = 25.6 * 0.1681
Therefore, the average maximum temperature in Cairo in February 2000 AD will be approximately 4.29 degrees C.