Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n ≥ 1?
2 answers:
<h2>Answer:</h2>
The sequence that could be partially defined by the given recursive formula is:
-10, -7.5 , -5 , -2.5 ,........
<h2>Step-by-step explanation:</h2>We are given a recursive formula as:
for n≥1
Hence, from the given options we will check the difference of which sequence is: 2.5
A)
2.5, 6.25, 15.625, 39.0625, …
6.25-2.5=3.75
15.625-6.25=9.375
As we could see that the common difference is not 2.5
Hence, option: A is incorrect.
B)
2.5, 5, 10, 20
5-2.5=2.5
10-5=5
20-10=10
As the common difference is not 2.5.
Hence, option: B is incorrect.
C)
–10, –7.5, –5, –2.5, …
-7.5-(-10)=-7.5+10=2.5
-5-(-7.5)=5+7.5=2.5
and -2.5-(-5)=-2.5+5=2.5
As the common difference is 2.5.
Hence, option: C is correct.
D)
-10, -25 , 6.25 , 156.25
-25-(-10)=-25+10= -15
As the common difference is not 2.5
Hence, option: D is incorrect.
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4. The point Z is the orthocenter of the triangle.
5. The length of GZ is of 9 units.
6. The length of OT is of 9.6 units.
<h3>What is the orthocenter of a triangle?</h3>The orthocenter of a triangle is the point of intersection of the three altitude lines of the triangle.
Hence, from the triangle given in the end of the answer, point Z is the orthocenter of the triangle.
For the midpoints connected through the orthocenter, the orthocenter is the midpoint of these segments, hence:
- The length of segment GZ is obtained as follows: GZ = 0.5 GU = 9 units. -> As z is the midpoint of the segment.
- The length of segment OT is obtained as follows: OT = 2ZT = 2 x 4.8 = 9.6 units.
The complete problem is given by the image at the end of the answer.
More can be learned about the orthocenter of a triangle at brainly.com/question/1597286
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Given:
The function is:
To find:
The value of .
Solution:
We have,
Putting , we get
On combining like terms, we get
Therefore, the required function is .