# Geometric progressiob

If the sum of four consective terms of geometric progression is 80 and arithmetic mean of second and fourth term is 30 then find terms?

Result

a =  2
b =  6
c =  18
d =  54

#### Solution:

$a+b+c+d = 80 \ \\ (b+d)/2 = 30 \ \\ b = qa \ \\ c = qb \ \\ d = qc \ \\ \ \\ a+c + 2 \cdot \ 30 = 80 \ \\ a+c = 20 \ \\ \ \\ a + aq^2 = 20 \ \\ \ \\ a(1+q^2) = 20 \ \\ qa(1+q^2) = 60 \ \\ q = 60/20 = 3 \ \\ \ \\ a = \dfrac{ 20 }{ 1+q^2 } = \dfrac{ 20 }{ 1+3^2 } = 2$
$b = q \cdot \ a = 3 \cdot \ 2 = 6$
$c = q \cdot \ b = 3 \cdot \ 6 = 18$
$d = q \cdot \ c = 3 \cdot \ 18 = 54$

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

#### Following knowledge from mathematics are needed to solve this word math problem:

Looking for help with calculating roots of a quadratic equation? Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

## Next similar math problems:

1. Before yesterday
He merchant adds a sale sign in his shop window to the showed pair of shoes in the morning: "Today by p% cheaper than yesterday. " After a while, however, he decided that the sign saying: "Today 62.5% cheaper than the day before yesterday". Determine the n
2. Heptagonal pyramid
A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm and the upper base of 14 cm. The altitude is 30 cm. Determine the weight in kg if the density of the wood is 0.10 grams/cm3.
3. Frustum of a cone
A reservoir contains 28.54 m3 of water when completely full. The diameter of the upper base is 3.5 m while at the lower base is 2.5 m. Determine the height if the reservoir is in the form of a frustum of a right circular cone.
4. Cylinder and its circumference
If the height of a cylinder is 4 times its circumference. What is the volume of the cylinder in terms of its circumference, c?
5. Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
6. Sides of right angled triangle
One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.
7. Coordinates of square vertices
I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C 'and D'. Thanks Peter.
8. The hemisphere
The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
9. Surface of the cylinder
Calculate the surface of the cylinder for which the shell area is Spl = 20 cm2 and the height v = 3.5 cm
10. Faces diagonals
If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.2, y=1.7, z=1.45
11. Compound interest 3
After 8 years, what is the total amount of a compound interest investment of \$25,000 at 3% interest, compounded quarterly? (interest is now dream - in the year 2019)
12. A rhombus
A rhombus has sides of length 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus.
13. Isosceles triangle 10
In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles.
14. Equation 23
Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
15. Geography tests
On three 150-point geography tests, you earned grades of 88%, 94%, and 90%. The final test is worth 250 points. What percent do you need on the final to earn 93% of the total points on all tests?
16. Medians in right triangle
It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides?