The number of terms in the given arithmetic sequence is n = 10. Using the given first, last term, and the common difference of the arithmetic sequence, the required value is calculated.
<h3>What is the nth term of an arithmetic sequence?</h3>
The general form of the nth term of an arithmetic sequence is
an = a1 + (n - 1)d
Where,
a1 - first term
n - number of terms in the sequence
d - the common difference
<h3>Calculation:</h3>
The given sequence is an arithmetic sequence.
First term a1 =
= 3/2
Last term an =
= 5/2
Common difference d = 1/9
From the general formula,
an = a1 + (n - 1)d
On substituting,
5/2 = 3/2 + (n - 1)1/9
⇒ (n - 1)1/9 = 5/2 - 3/2
⇒ (n - 1)1/9 = 1
⇒ n - 1 = 9
⇒ n = 9 + 1
∴ n = 10
Thus, there are 10 terms in the given arithmetic sequence.
learn more about the arithmetic sequence here:
brainly.com/question/503167
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Disclaimer: The given question in the portal is incorrect. Here is the correct question.
Question: If the first and the last term of an arithmetic progression with a common difference are
,
and 1/9 respectively, how many terms has the sequence?
(8,1) since the midpoint is 3 away from the endpoint, it must also be 3 away from the other endpoint
Answer:
2.10 s, 10.40 s.
Step-by-step explanation:
We know that the height of the rocket is given by the function:
![h=-16t^2+200t](https://tex.z-dn.net/?f=h%3D-16t%5E2%2B200t)
We are asked to find the time for which the height of the rocket will be 350 ft. So, for that moment, we know the height but we don't know the time; however, we know that the equation can help us to find the time, doing h=350:
![350=-16t^2+200t](https://tex.z-dn.net/?f=350%3D-16t%5E2%2B200t)
The last is a quadratic equation, which can be put in the form
and solved applying the formula:
![t=\frac{-b+-\sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B-b%2B-%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D)
So, let's put the equation on the form
adding
and subtracting
to each side of the equation; the result is:
![16t^2-200t+350=0](https://tex.z-dn.net/?f=16t%5E2-200t%2B350%3D0)
So, we note that a=16, b=-200, and c=350.
Then,
![t_1=\frac{200-\sqrt{200^2-4*16*350} }{2*16}=2.10](https://tex.z-dn.net/?f=t_1%3D%5Cfrac%7B200-%5Csqrt%7B200%5E2-4%2A16%2A350%7D%20%7D%7B2%2A16%7D%3D2.10)
![t_2=\frac{200+\sqrt{200^2-4*16*350} }{2*16}=10.40](https://tex.z-dn.net/?f=t_2%3D%5Cfrac%7B200%2B%5Csqrt%7B200%5E2-4%2A16%2A350%7D%20%7D%7B2%2A16%7D%3D10.40)
According to the equation, that are the times for which the height will be 350 ft; that is because the rocket is going to ascend and then to fail again to the ground.
Answer:
m m m m m m
Step-by-step explanation:
mmmmmmmmm m m m m m m mm m m m m m m
First find the slope of the line = (y2 - y1) / (x2 - x1) where the 2 points are (x1, y1 and (x2, t2).
Then substitute the values of the slope (m) and one of the points into the point-slope formula
y - y1 = m(x - x1)