Find the next two terms in the given sequence, then write it in recursive form. A.) {7,12,17,22,27,...} B.) { 3,7,15,31,63,...}
iren [92.7K]
Answer:
A) a_n = 5n + 2
B) a_n = (2^(n + 1)) - 1
Step-by-step explanation:
A) The sequence is given as;
{7,12,17,22,27,...}
The differences are:
5,5,5,5.
This is an arithmetic sequence following the formula;
a_n = a_1 + (n - 1)d
d is 5
Thus;
a_n = a_1 + (n - 1)5
Now, a_1 = 7. Thus;
a_n = 7 + 5n - 5
a_n = 5n + 2
B) The sequence is given as;
{ 3,7,15,31,63,...}
Now, let's write out the differences of this sequence:
Differences are:
4, 8, 16, 32
This shows that it is a geometric sequence with a common ratio of 2.
In the given sequence, a_1 = 3 and a_2 = 7 and a_3 = 15
Thus, a_2 = 2a_1 + 1
Also, a_(2 + 1) = 2a_2 + 1
Combining both equations, we can deduce that: a_(n + 1) = 2a_n + 1
Thus; a_n can be expressed as:
a_n = (2^(n + 1)) - 1
Area=Length x Width (A=LW)
A=30.5 x 12.5
A=381.25
Answer:
The z-score for this kernel is -2.3
Step-by-step explanation:
* Lets revise how to find the z-score
- The rule the z-score is z = (x - μ)/σ , where
# x is the score
# μ is the mean
# σ is the standard deviation
* Lets solve the problem
- The popping-times of the kernels in a certain brand of microwave
popcorn are normally distributed
- The mean is 150 seconds
- The standard deviation is 10 seconds
- The first kernel pops is 127 seconds
- We want to find the z-score for this kernel
∵ z-score = (x - μ)/σ
∵ x = 127
∵ μ = 150
∵ σ = 10
∴ z-score = (127 - 150)/10 = -23/10 = -2.3
* The z-score for this kernel is -2.3
Answer:
18/24 for the first one
Step-by-step explanation:
7.77777777 repeating
Irrational numbers are:
Numbers that repeat
7.7777777 repeats the number 7 after the decimal
Numbers that CANNOT be written as a simple fraction.
7.7777777 cannot be written as a fraction in simplest form.
Answer = 7.777777777 repeating
~Aamira~
Hope this helped :)
