Infinite geometric series - practice problems

Direction: Solve each problem carefully and show your solution in each item.

Number of problems found: 29

Series and sequences
Find a fraction equivalent to the recurring decimal. 0.435643564356
Determine 4113
Determine the sum of an infinite series: 1/3 + 1/9 + 1/27 + 1/81 ...
Decimal to fraction
Write decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures.
Sum of GP members
Determine the sum of the GP 30, 6, 1.2, to 5 terms. What is the sum of all terms (to infinity)?
Fraction
Fraction frac(0, overline(38))(0,38) write as fraction a/b, a, b is integers numerator/denominator.
Sum of series
Determine the 6-th member and the sum of a geometric series: 5-4/1+16/5-64/25+256/125-1024/625+....
Remainder 34441
Find the remainder after division when we divide the sum of 1! +2! +3! +. ... . +300! number 13.
Quantities 60183
Determine the remaining quantities in the finite geometric sequence, given: n = 4, an = 12.5, sn = 187.5, a1 = ?, q =?
Infinite decimal
Imagine the infinite decimal number 0.99999999... That is a decimal and her endless series of nines. Determine how much this number is less than the number 1. Thank you in advance.
Equation 6738
Solve the given equation in the set N: 1 - x + x² - x³ + x⁴ - x⁵ +…. + = 1/3
Flower series
Every day, the flower develops two new flowers, and each of these new blossoms also bears two flowers each day. After eight days, how many blooms are already present in the garden?
Geometric series
How many terms of the geometric series 8+4+2+1+0.5+... must be taken for the sum to get within 10 to the power minus 4 of its sum to infinity?
Saving per cents
The first day I saved 1 cent and every following day a cent more. How many do I save in one year (365 days)?
Descending 81797
The sum of the first two terms of the descending geometric sequence is five quarters, and the sum of the infinite geometric series formed from it is nine quarters. Write the first three terms of the geometric sequence.
Ten dices
When you hit ten dice simultaneously, you get an average of 35. How much do you hit if every time you get six, you're throwing the dice again?
Annual interest
A loan of 10 000 euros is to be repaid in annual payments over ten years. Assuming a fixed 10% annual interest rate compounded annually, calculate: (a) the amount of each annual repayment (b) the total interest paid.
Single-celled 4642
Guts (a single-celled organism under ideal conditions divides into two littles every 27 hours on average. How many would there be in 7 days if all the littles remained alive?
Population growth
How many people will be on Earth from two people for 5,000 years if every couple always has four children (2 boys and two girls) at the age of 25-35, and every man will live 75 years?
Miraculous tree
The miraculous tree grows so fast that the first day increases its height by half the total height of the second day by the third, the third day by a quarter, etc. How many times will it increase its height after 6 days?
Recursion squares
In the square, ABCD has inscribed a square so that its vertices lie at the centers of the sides of the square ABCD. The procedure of inscribing the square is repeated this way. The side length of the square ABCD is a = 22 cm. Calculate: a) the sum of peri

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