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How do you find the common ratio in a geometric progression when the sum of the first 20 terms is 244 times the sum of its first 10 terms?
Sum of 10 terms is n(r10-1)/(r-1) where n = 1st term. Sum of 20 is n(r20-1)/(r-1) so ratio is (r20-1)/(r10-1). Let r10 be called x. So the ratio is (x2-1)/(x-1) which is just x+1, so x=243. The common ratio is therefore the 10th root of this. Which is square root of 3.
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What is the common ratio of the geometric progression?
The common ratio is the ratio of the nth term (n > 1) to the (n-1)th term. For the progression to be geometric, this ratio must be a non-zero constant.
How do you find the ratio in the geometric progression?
Divide any term, except the first, by the term before it.
What do the following numbers have in sequence - 512-256-128-64?
It is a geometric progression with common ratio 0.5
What is the difference between arithmetic progression and geometric progression?
In an arithmetic progression the difference between each term (except the first) and the one before is a constant. In a geometric progression, their ratio is a constant. That is, Arithmetic progression U(n) - U(n-1) = d, where d, the common difference, is a constant and n = 2, 3, 4, ... Equivalently, U(n) = U(n-1) + d = U(1) + (n-1)*d Geometric progression U(n) / U(n-1) = r, where r, the common ratio is a non-zero constant and n = 2, 3, 4, ... Equivalently, U(n) = U(n-1)*r = U(1)*r^(n-1).
What number is missing from the following sequence 1875-375-75--3?
15. It's a Geometric Progression with a Common Ratio of 1/5 (or 0.2).
What is the common ratio of the geometric progression?
The common ratio is the ratio of the nth term (n > 1) to the (n-1)th term. For the progression to be geometric, this ratio must be a non-zero constant.
What is the sum of the first 15 terms of an arithmetic?
For an Arithmetic Progression, Sum = 15[a + 7d].{a = first term and d = common difference} For a Geometric Progression, Sum = a[1-r^15]/(r-1).{r = common ratio }.
How do you find the ratio in the geometric progression?
Divide any term, except the first, by the term before it.
What do the following numbers have in sequence - 512-256-128-64?
It is a geometric progression with common ratio 0.5
What are scientific words that start with g?
Geology, Geography, Geometry, Gems, Gold, Gadolinium, Gallium, Germanium, Graduated Cylinder, Gametes, Gauges, Geotropism, Gigabytes, Gigapascal, Gluon, and Gravity.
How can you tell if a infinite geometric series has a sum or not?
The geometric series is, itself, a sum of a geometric progression. The sum of an infinite geometric sequence exists if the common ratio has an absolute value which is less than 1, and not if it is 1 or greater.
What is the difference between arithmetic progression and geometric progression?
In an arithmetic progression the difference between each term (except the first) and the one before is a constant. In a geometric progression, their ratio is a constant. That is, Arithmetic progression U(n) - U(n-1) = d, where d, the common difference, is a constant and n = 2, 3, 4, ... Equivalently, U(n) = U(n-1) + d = U(1) + (n-1)*d Geometric progression U(n) / U(n-1) = r, where r, the common ratio is a non-zero constant and n = 2, 3, 4, ... Equivalently, U(n) = U(n-1)*r = U(1)*r^(n-1).
What number is missing from the following sequence 1875-375-75--3?
15. It's a Geometric Progression with a Common Ratio of 1/5 (or 0.2).
What is the pattern for a half a quarter and an eighth?
It's a geometric progression with the initial term 1/2 and common ratio 1/2. The infinite sum of the series is 1.
What is the 7th term in the geometric sequence whose first term is 5 and the common ratio is -2?
Find the 7th term of the geometric sequence whose common ratio is 1/2 and whose first turn is 5
Can common ratio be 1 in geometric progression?
if a number is multiplied by 1, then it does not change, it is Still the same number. A ratio of 1 is impossible . The ratio between two quantities must always be greater than 1 otherwise there is no difference between them.
What will be the first term and the common ratio of geometric progression whose 6th and 9th terms are 160 and 1280 respectively?
ar5 = 160 ar8 = 1280 so r3 = 1280/160 = 8 and so r = 2 then, ar5 = 160 gives a = 160/32 = 5 First term = a = 5 Common ratio = r = 2
