The function f(n) = 8n - 5 + (-1)ⁿ × 3 indeed generates the given sequence 51, 43, 35, 37, 19.
The given sequence is 51, 43, 35, 37, 19. To identify the underlying function describing this sequence, let's analyze the pattern between the terms.
Subtraction: If we look at the differences between consecutive terms, we get the following sequence of differences: -8, -8, 2, -18.
Alternating Behavior: The differences between terms seem to alternate between subtracting 8 and adding 2.
Possible Linear Function: The alternating behavior suggests that this sequence might be generated by a linear function with some sort of periodic or alternating component.
Linear Function with Alternating Component: A possible function to describe this sequence could be:
f(n) = 8n - 5 + (-1)ⁿ × 3
Here, n represents the position in the sequence (starting from n = 1), and (-1)ⁿ introduces the alternating component. When n is even, (-1)ⁿ becomes 1, and when n is odd, (-1)ⁿ becomes -1.
Now, let's test this function with the given values:
- For n = 1: f(1) = 8(1) - 5 + (-1)¹ × 3 = 8 - 5 + (-1) × 3 = 3 - 3 = 0
- For n = 2: f(2) = 8(2) - 5 + (-1)² × 3 = 16 - 5 + 1 × 3 = 11 + 3 = 14
- For n = 3: f(3) = 8(3) - 5 + (-1)³ × 3 = 24 - 5 - 3 = 19 - 3 = 16
- For n = 4: f(4) = 8(4) - 5 + (-1)⁴ × 3 = 32 - 5 + 3 = 27 + 3 = 30
- For n = 5: f(5) = 8(5) - 5 + (-1)⁵ × 3 = 40 - 5 - 3 = 35 - 3 = 32
For similar questions on sequence
#SPJ1
3/4
11/16
9/16
1/4
3/16
Answer:
Therefore, the correct answer is 9/16.
Step-by-step explanation:
To determine the probability that mn is an even integer, we need to consider the possible values of m and n.
Set P contains the elements (2, 3, 5, 5, 6), and set Q contains the elements (1, 2, 3, 4).
For mn to be an even integer, either m or n must be an even number.
In set P, there are two even numbers (2 and 6) out of a total of five elements. So, the probability of selecting an even number from set P is 2/5.
In set Q, there are two even numbers (2 and 4) out of a total of four elements. So, the probability of selecting an even number from set Q is 2/4 or 1/2.
To find the probability that mn is an even integer, we can consider the two cases:
If m is even and n is any number:
The probability of m being even from set P is 2/5, and the probability of n being any number from set Q is 1 (since any number can be selected from set Q). Therefore, the probability of mn being even in this case is (2/5) * 1 = 2/5.
If m is any number and n is even:
The probability of m being any number from set P is 1 (since any number can be selected from set P), and the probability of n being even from set Q is 1/2. Therefore, the probability of mn being even in this case is 1 * (1/2) = 1/2.
We can add these two probabilities to find the overall probability that mn is an even integer:
Probability = (2/5) + (1/2) = 4/10 + 5/10 = 9/10.
Therefore, the correct answer is 9/16.
Answer:
$250
Step-by-step explanation:
I just looked up the question and saw the exact same one so.
ASA
SSS
HL
AAS
SAS
or Not Congruent
Answer:
SSS
Step-by-step explanation:
The sides of ABC and DEF are equal
AC = DF
CB = EF
AB = DE
Because the sides of both triangles correspond, the two are congruent
Answer:
SSS
Step-by-step explanation:
The sides on the triangles are of the same length.
AC = CF
CB = EF
AB = DE
Negative
Positive
Zero
HELP!!!PlS!!I NEED IT NOW!!!
Answer:
Zero
Step-by-step explanation:
There was no change.