-5, 20, -80, 320, ... is a geometric sequence a. Find the common ratio, b. Write its recursive rule c. Write its explicit rule.W
1 answer:
a.
In order to find the common ratio, we just need to divide a term by the term that comes before it.
So using the terms 20 and -5, we have:
b.
The recursive rule can be found with the formula:
Where an is the nth term and q is the ratio. So we have:
c.
The explicit rule can be written as:
Where an is the nth term, a1 is the first term and q is the ratio. So:
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It is depending upon multiplication of values to variable and values of numbers again. Here the answer is Option B) 11x + 4. Here is my process on this equating expression.
For this we have to apply the law of distribution or the distributive law, in this we distribute the parentheses into the brackets to further expand them, we further eliminate the bracketed groups and perform the calculations. So, it is stating that, for any number, variable or a quantity if multiplied into a bracketed expression yields two products of multiplication of two quantities; one being the first quantity outside the brackets and two separately distinguished quantities inside the brackets. They are furthermore subtracted by the first quantity to that of the second quantity to obtain and achieve the distributive law.
If I were to express it through mathematical LaTeX Expressions, it will be represented as the first quantity as a variable of "a" where it can exhibit a value or a variable or a term or rule, etc. and then inside the brackets represented as "b" and "c".
Performing the law of distribution of values, variables, etc. It is demonstrated as:
We are given the values of the variables as a separate context and addition of two expressions. So, for both of them:
Apply the following distribution law to expand the values onto variables and numbered values inside the brackets.
So, the variable "a", "b" and "c"; For First Expression is: a = 3, b = x and c = 4.
And, Similarly, for the variable of "a", "b" and "c", For Second Expression is: a = 8, b = x and c = 2.
Therefore, According to our distributive law of expanding the components will directly yield us:
Regroup the terms for a better visualisation and a clearer understanding for similarities between the terms; it makes it more easier to proceed further. So:
All we did, was to separate the variable attached numbered values and shift it on one side; And, separating or shifting the values without variables to the other side.
Hope it helps.
For this we have to apply the law of distribution or the distributive law, in this we distribute the parentheses into the brackets to further expand them, we further eliminate the bracketed groups and perform the calculations. So, it is stating that, for any number, variable or a quantity if multiplied into a bracketed expression yields two products of multiplication of two quantities; one being the first quantity outside the brackets and two separately distinguished quantities inside the brackets. They are furthermore subtracted by the first quantity to that of the second quantity to obtain and achieve the distributive law.
If I were to express it through mathematical LaTeX Expressions, it will be represented as the first quantity as a variable of "a" where it can exhibit a value or a variable or a term or rule, etc. and then inside the brackets represented as "b" and "c".
Performing the law of distribution of values, variables, etc. It is demonstrated as:
We are given the values of the variables as a separate context and addition of two expressions. So, for both of them:
Apply the following distribution law to expand the values onto variables and numbered values inside the brackets.
So, the variable "a", "b" and "c"; For First Expression is: a = 3, b = x and c = 4.
And, Similarly, for the variable of "a", "b" and "c", For Second Expression is: a = 8, b = x and c = 2.
Therefore, According to our distributive law of expanding the components will directly yield us:
Regroup the terms for a better visualisation and a clearer understanding for similarities between the terms; it makes it more easier to proceed further. So:
All we did, was to separate the variable attached numbered values and shift it on one side; And, separating or shifting the values without variables to the other side.
Hope it helps.