Antecedent is the first term in a ratio .
The first term is 10. Dividing (say) the 3rd term by the 2nd term gives 40/20 = 2 Dividing any two successive terms in this manner results in the same answer. Then 2 is the common ratio. The general formula for the nth term of a Geometric Progression or Series is :- a(n) = ar^n-1.....where a is the first term and r is the common ratio. For the pattern provided, a(n) = 10 x 2^n-1
The numerator of the second ratio and the denominator of the first ratio are called the means, and the numerator of the first ratio and the denominator of the second ratio are called the extremes. The product of the means equals the product of the extremes.
As 21 is 3 x 7 the ratio 7:21 = 1:3
I guess you mean the ratio of the areas; it depends if the 2 rectangles are "similar figures"; that is their matching sides are in the same ratio. If they are similar then the ratio of their areas is the square of the ratio of the sides.
(1/sq rt 5)((1+sq rt 5)/2)n - (1/sq rt 5)((1-sq rt 5)/2)n This is based on the golden ratio (1+sq rt 5)/2) because the ratio of 2 Fibonacci terms approaches the golden ratio as the 2 terms used get larger. IE the ratio ot the 10th term to the 9th term is 55/34 = 1.61765 and the golden ratio is approx. 1.61803. When using this formula if your calculator does not round, you will round to get the appropriate Fibonacci number.
It is a*r^4 where a is the first term and r is the common ratio (the ratio between a term and the one before it).
no
27
You start with the number 4, then multiply with the "common ratio" to get the next term. That, in turn, is multiplied by the common ratio to get the next term, etc.
11.27357
It is 1062882.
-1,024
Divide any term, except the first, by the term before it.
36
Find the 7th term of the geometric sequence whose common ratio is 1/2 and whose first turn is 5
The use of the expression 'common ratio' means that the sequence is a Geometric series where the terms are of the form a, ar ar2, ar3, ...arn-1 where a is the first term and r is the common ratio. The third term, a3 = 3 x 32 = 3 x 9 = 27
In a Geometric Sequence each term is found by multiplying the previous term by a common ratio except the first term and the general rule is ar^(n-1) whereas a is the first term, r is the common ratio and (n-1) is term number minus 1