# 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:

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

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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

Be the first to comment!

Tips to related online calculators
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. Six terms
Find the first six terms of the sequence a1 = -3, an = 2 * an-1
2. GP members
The geometric sequence has 10 members. The last two members are 2 and -1. Which member is -1/16?
3. Coefficient
Determine the coefficient of this sequence: 7.2; 2.4; 0.8
4. Geometric progression 2
There is geometric sequence with a1=5.7 and quotient q=-2.5. Calculate a17.
5. Expression with powers
If x-1/x=5, find the value of x4+1/x4
6. Algebra
X+y=5, find xy (find the product of x and y if x+y = 5)
7. The product
The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number
8. Holidays - on pool
Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
9. Equation 23
Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
10. Equation
Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
11. Square root 2
If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
12. Roots
Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
13. Discriminant
Determine the discriminant of the equation: ?
14. Solve 3
Solve quadratic equation: (6n+1) (4n-1) = 3n2
15. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?