Which explains why the sequence 81, 3, 1/9,... is arithmetic or geometric?
A)The sequence is arithmetic because it decreases by a factor of 1/27
B)The sequence is geometric because it decreases by a factor of 1/27
C)The sequence is arithmetic because it decreases by a factor of 3. THIS ONE
D)The sequence is geometric because it decreases by the factor of 3.
Write an expression to describe a rule for the sequence. Then find the 100th term in the sequence.
3, 10, 17, 24, 31, 38,...
A)n + 7;707
B)7n; 700
C)7n-4; 696 THIS ONE
D)6n-4; 596
The time between a lightning flash and the following thunderclap may be used to estimate, in kilometers, how far away a storm is. How far away is a storm if 12 seconds elapse between the lightning and the thunderclap?
Use the formula d=t/3, where t is the time, in seconds, between the flash and the thunderclap.
A)4 kilometers
B)5 kilometers
C)15 kilometers
D)36 kilometers THIS ONE
you got the middle one
take another look at the first and last
81*1/27 = 9
9 * 1/27 = 1/3
http://www.mathsisfun.com/algebra/sequences-sums-geometric.html
3 + 7(n-1) = 3 + 7 n-7 = 7 n - 4 correct
https://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html
NO!!!!
about 330 meters/second for sound in air
d = 330 * 12 = 3960 meters about 4 km
The correct answers are:
1) The sequence 81, 3, 1/9,... is geometric because it decreases by a factor of 1/27. The correct answer is B) The sequence is geometric because it decreases by a factor of 1/27.
2) The expression to describe a rule for the sequence 3, 10, 17, 24, 31, 38,... is 7n - 4.
Therefore, the 100th term can be calculated by substituting n = 100 into the expression:
7(100) - 4 = 696
So, the 100th term in the sequence is 696. The correct answer is C) 7n-4; 696.
3) If 12 seconds elapse between the lightning and the thunderclap, the storm is estimated to be 36 kilometers away.
Using the formula d = t/3, where t is the time in seconds between the flash and the thunderclap, we substitute t = 12:
d = 12/3 = 4 kilometers
Therefore, the storm is estimated to be 4 kilometers away. The correct answer is A) 4 kilometers.
To determine whether the sequence 81, 3, 1/9,... is arithmetic or geometric, we need to observe the pattern of the terms.
In an arithmetic sequence, each term is obtained by adding (or subtracting) a constant value to the previous term.
In a geometric sequence, each term is obtained by multiplying (or dividing) the previous term by a constant value.
By examining the sequence, we can see that each term is obtained by dividing the previous term by 27, which is equal to (1/27).
Therefore, the correct answer is B) The sequence is geometric because it decreases by a factor of 1/27.
For the second question, we are given the sequence 3, 10, 17, 24, 31, 38,... and we need to find the expression that describes the rule for the sequence and then determine the 100th term.
By observing the sequence, we can see that each term is obtained by adding 7 to the previous term.
Therefore, the correct expression to describe the rule for the sequence is C) 7n - 4.
To find the 100th term, we substitute n = 100 into the expression:
7(100) - 4 = 700 - 4 = 696
Therefore, the 100th term in the sequence is 696, and the correct answer is C) 7n-4; 696.
For the last question, we are given the formula d = t/3, where d represents the distance in kilometers and t represents the time in seconds between the lightning and the thunderclap.
We are given that 12 seconds elapsed between the lightning flash and the thunderclap, so we can substitute t = 12 into the formula:
d = 12/3 = 4 kilometers
Therefore, the storm is 4 kilometers away, and the correct answer is A) 4 kilometers.