Question

The sum of an infinite geometric series is 13,5 The sum of the same series, calculated from the third term is 1,5. Q. Calculate r if r>0.

216

likes
1079 views

Answer to a math question The sum of an infinite geometric series is 13,5 The sum of the same series, calculated from the third term is 1,5. Q. Calculate r if r>0.

Expert avatar
Eliseo
4.6
109 Answers
Let's denote the first term of the infinite geometric series as 'a' and the common ratio as 'r'. The sum of an infinite geometric series is given by the formula: S = a / (1 - r) Given that the sum of the series is 13.5, we have: 13.5 = a / (1 - r) .....(Equation 1) We are also given that when the series is calculated from the third term, the sum is 1.5. To calculate the sum from the third term, we need to multiply the third term by the sum of a geometric series starting from the first term. The sum of a geometric series starting from the first term is given by: S = a / (1 - r) So, the sum from the third term is: 1.5 = (a * r^2) / (1 - r) .....(Equation 2) To solve this system of equations, we can divide Equation 1 by Equation 2: (13.5) / (1.5) = (a / (1 - r)) / ((a * r^2) / (1 - r)) 9 = (a / (1 - r)) * ((1 - r) / (a * r^2)) 9 = 1 / (r^2) Taking the reciprocal of both sides: 1/9 = r^2 Taking the square root of both sides (since r > 0): r = 1/3 Therefore, the common ratio 'r' for the given infinite geometric series is 1/3.

Frequently asked questions (FAQs)
What is the value of sinh(arcsinh(3)) - tanh(arctanh(5))?
+
What are the characteristics of an ellipse with an equation (x-h)^2/a^2 + (y-k)^2/b^2 = 1?
+
What is the Pythagorean theorem used for?
+
New questions in Mathematics
a to the power of 2 minus 16 over a plus 4, what is the result?
Simplify the expression sin³(x)+cos³(x), using trigonometric functions
the value of sin 178°58'
Exercise 4 - the line (AC) is perpendicular to the line (AB) - the line (EB) is perpendicular to the line (AB) - the lines (AE) and (BC) intersect at D - AC = 2.4 cm; BD = 2.5 cm: DC = 1.5 cm Determine the area of triangle ABE.
Derivative of x squared
(5u + 6)-(3u+2)=
You are planning to buy a car worth $20,000. Which of the two deals described below would you choose, both with a 48-month term? (NB: estimate the monthly payment of each offer). i) the dealer offers to take 10% off the price, then lend you the balance at an annual percentage rate (APR) of 9%, monthly compounding. ii) the dealer offers to lend you $20,000 (i.e., no discount) at an APR of 3%, monthly compounding.
There are 162 students enrolled in the basic mathematics course. If the number of women is 8 times the number of men, how many women are there in the basic mathematics course?
Scores are normally distributed with a mean of 25 and standard deviation of 5. Find the probability that sixteen randomly selected students have a mean score that is less than 24.
Show this compound proposition to be true or false. Paris is the capital of England or Rome is the capital of Italy
Next%C3%B3n%2C+we+are+given+a+series+of+Tri%C3%A1angles+Right%C3%A1angles+%3Cbr%2F%3Ey+in+each+one+of+them+ are+known+2%28two%29+measurements+of+sides.+%3Cbr%2F%3Elet's+determine+all+trigonom%C3%A9tric+ratios.
Congratulations, you have saved well and are ready to begin your retirement. If you have $1,750,000.00 saved for your retirement and want it to last for 40 years, and will earn 10.8% compounded monthly: What is the amount of the monthly distribuion? 216.50 How much interest is earned in retirement?
Show work on 4108 divided by 4
-5x=115
write in set builder notation { 1,3,9,27,81,243,...}
Kayla started a book club at her school. The number of girls in the book club was one more than twice the number of boys. If there are 15 girls in the book club, how many boys are in the club?
In a school playground When going out for recess, 80 men and 75 women coexist, the Patio measures 10 meters For 40 meters (what will be the population density in the break
7-1=6 6x2=12 Explain that
A rectangular swimming pool has a length of 14 feet, a width of 26 feet and a depth of 5 feet. Round answers to the nearest hundredth as needed. (a) How many cubic feet of water can the pool hold? cubic feet (b) The manufacturer suggests filling the pool to 95% capacity. How many cubic feet of water is this? cubic feet
Mark is gluing a ribbon around the sides of a picture frame. The frame is 11 inches long and 7 includes wide. How much ribbon does Mark need?