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
Answer:
The train would travel 880 km in 11 hours.
Step-by-step explanation:
To find the inverse, interchange the variables and solve for y.
f^−1(x)=−25+5x/2
Answer:
$ 0.8.
Step-by-step explanation:
1) if to assume, 'c' - price of the coffee and 'd' - price of the doughnuts, then
2) it is possible to write the equation 1 (when five MinB enter): 3d+5c=3.3;
3) it is possible to write the equation 2 (when three aliens entered): 4d+3c=2.75;
5) if c=0.45 and d=0.35, then Ag.Z. paid 0.35+0.45=$ 0.8.
Answer: continuous random variable.
Step-by-step explanation:
A discrete random variable is defined as a random variable which consists of countable number. Examples include numbers of shoes, number of sales etc.
A continuous random variable is a random variable whereby the data can take several values. It is a random variable that takes time into consideration.
Therefore, the amount of time six randomly selected volleyball players play during a game will be a continuous random variable since time so involved.
