A sequence can be generated by using a n=3a(n-1) where a1=6 and n is a whole number greater than 1.what are the first four terms of the sequence?
A. 6,9,12,15
B.6,18,54,162
C.6,12,18,24
D.6,36,216,1296
To generate the terms of the sequence, we start with a1 = 6 and use the formula n = 3a(n-1).
The first term is a1 = 6.
To find the second term, we substitute n = 2 into the formula:
a2 = 3a(2-1) = 3a1 = 3*6 = 18.
To find the third term, we substitute n = 3 into the formula:
a3 = 3a(3-1) = 3a2 = 3*18 = 54.
To find the fourth term, we substitute n = 4 into the formula:
a4 = 3a(4-1) = 3a3 = 3*54 = 162.
Therefore, the first four terms of the sequence are 6, 18, 54, and 162.
So, the correct answer is B. 6, 18, 54, 162.
In a sequence of numbers,
A3=1,a4=4,a5=8,a6=12, and a7=16. Based on this information, which equation can be used to find the n^th term in the sequence, an?
A. A n =-12n+4
B.a n = 12n - 4
C.a n =4n -12
D. A n= -4n+12
To find the equation for the nth term of the sequence, we need to look for a pattern in the given terms.
Looking at the given terms, we can see that the sequence is increasing by 3 in each step. Therefore, the common difference between the terms is 3.
We can also observe that the first term, a3, is 1, and the subsequent terms a4, a5, a6, a7 increase by 3 from the previous term.
Based on this pattern, we can determine the equation for the nth term of the sequence as follows:
an = a3 + (n - 3)d
where a3 is the first term, d is the common difference (3 in this case), and n is the position of the term.
Substituting the values, we get:
an = 1 + (n - 3)3
Simplifying this equation gives:
an = 1 + 3n - 9
an = 3n - 8
Therefore, the correct equation to find the nth term of the sequence is option:
C. an = 3n - 8
Apples at the local farmers’s market cost 1.25 per pound. Write a function rule f that gives the total cost of apples in terms of the number of pounds, x.
F(x)=
The function rule that gives the total cost of apples in terms of the number of pounds, x, can be written as:
F(x) = 1.25x
This means that the total cost, F(x), is equal to the price per pound, 1.25, multiplied by the number of pounds, x.
The price of a pizza is $7.99 plus an additional $1.35 for each topping.
Write a function rule f that gives the total price as a function of the number of toppings, x.
F(x)=
The function rule that gives the total price of a pizza as a function of the number of toppings, x, can be written as:
F(x) = 7.99 + 1.35x
This means that the total price, F(x), is equal to the base price of $7.99 plus $1.35 multiplied by the number of toppings, x.