# Geometric sequence 5

About members of geometric sequence we know:

$3 a$5:a3 = 27:25

$7 a$3 +5 a7 = 1 : 564

Calculate a1 (first member) and q (common ratio or q-coefficient)

Result

q =  0.6
a1 =  204.84658

#### Solution:

$3 a_5:a_3 = 27:25 \ \\ 3 a_1 q^4 : (a_1 q^2 ) = 27:25 \ \\ 3 q^2 = 27/25 \ \\ q^2 = 9/25 \ \\ q = \pm 3/5 \ \\ q_1 = - 3/5 \ \\ q_2 = 3/5 \ \\ \ \\$
$7 a_3 +5 a_7 = 1 : 564 \ \\ 7a_1q^2+5a_1q^6 = 1:564 \ \\ a_1 (7q^2+5q^6) = 1:564 \ \\ \ \\ a_1 = 564 : (63/25 + 729/3125) \ \\ a_1= 204.84658$

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
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. Geometric progression 2
There is geometric sequence with a1=5.7 and quotient q=-2.5. Calculate a17.
2. Six terms
Find the first six terms of the sequence a1 = -3, an = 2 * an-1
3. Sequence
Find the common ratio of the sequence -3, -1.5, -0.75, -0.375, -0.1875. Ratio write as decimal number rounded to tenth.
4. Insert into GP
Between numbers 5 and 640 insert as many numbers to form geometric progression so sum of the numbers you entered will be 630. How many numbers you must insert?
5. Geometric progression 4
8,4√2,4,2√2
6. Null points
Calculate the roots of the equation: ?
7. Warehouses
In the three warehouses, a total of 70 tons of grain was stored. In the second warehouse was stored 8.5t less and in the third 3.5t more than in the first. How many tons of grain was stored in each warehouse?
8. Three workshops
There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?
9. Ball game
Richard, Denis and Denise together scored 932 goals. Denis scored 4 goals over Denise but Denis scored 24 goals less than Richard. Determine the number of goals for each player.
10. Linsys2
Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
11. 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?
12. Men, women and children
On the trip went men, women and children in the ratio 2:3:5 by bus. Children pay 60 crowns and adults 150. How many women were on the bus when a bus was paid 4,200 crowns?
13. Children
The group has 42 children. There are 4 more boys than girls. How many boys and girls are in the group?
14. Stones 3
Simiyu and Nasike each collected a number of stones in an arithmetic lesson. If Simiyu gave Nasike 5 stones, Nasike would have twice as many stones as Simiyu. If initially, Simiyu had five stones less than Nasike how many stones did each have?
15. Legs
Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?
16. Intercept with axis
F(x)=log(x+4)-2, what is the x intercept
17. Linear imaginary equation
Given that ? "this is z star" Find the value of the complex number z.