Answer:
a. a[1] = 3; a[n] = 2a[n-1]
b. a[n] = 3·2^(n-1)
c. a[15] = 49,152
Step-by-step explanation:
Each term of the given sequence is 2 times the previous term. (This description is the basis of the recursive formula.) That is, the terms of the given sequence have a common ratio of 2. This means the sequence is geometric, so the formulas for explicit and recursive rules for a geometric sequence apply.
The first term is 3, and the common ratio is 2.
<h3>(a)</h3>
The recursive rule is ...
a[1] = 3
a[n] = 2×a[n-1]
__
<h3>(b)</h3>
The explicit rule is ...
a[n] = a[1]×r^(n-1)
a[n] = 3×2^(n-1)
__
<h3>(c)</h3>
The 15th term is ...
a[15] = 3×2^(15-1) = 3×2^14
a[15] = 49,152
Answer:
The integer is -16
Step-by-step explanation:
The first scuba diver is 23 feet below sea level. THe second is 7 feet closer.
23 - 7 = 16. He is still under sea level, so it would be -16
Answer:
the length of an arc = 10π ft.
Step-by-step explanation:
The length of an arc with angle Θ and radius r will be equal r * Θ
note the angle must be in radian
Given: Θ = 180° = π and radius = r = 10 ft.
<u>So, the length of the arc = π * 10 = 10π ft.</u>
Answer: SECOND OPTION.
Step-by-step explanation:
It is important to remember that, by definition, the "Resultant vector " is the vector obtained by adding two or more vectors.
For this exercise you need to use the formula for calculate the magnitude of the resultant vector obtained by adding the vectors "a" and "b" shown in the picture attached:
Where "c" is the magnitude of the resultant vector asked in the exercise.
You need to analyze the graph given in the exercise.
You can identify that:
Then the next step, knowing which are "a" and "b", is to substitute values into the formula given at the beginning of this explanation, as following:
Finally, evaluating, you get that "c" is:
Answer:
0.778
Step-by-step explanation:
Round up if this number is greater than or equal to 5 and round down if it is less than 5.
