5th grade math. correct answer will be marked brainliest.

Dont really understand how to do this

bija089 [108]

Answers:

$t_{10} = -22 \ \text{ and } S_{10} = -85$

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Explanation:

$t_1 = \text{first term} = 5\\t_2 = \text{first term}-3 = t_1 - 3 = 5-3 = 2$

Note we subtract 3 off the previous term (t1) to get the next term (t2). Each new successive term is found this way

$t_3 = t_2 - 3 = 2-3 = -1\\t_4 = t_3 - 3 = -1-3 = -4$

and so on. This process may take a while to reach $t_{10}$

There's a shortcut. The nth term of any arithmetic sequence is

$t_n = t_1+d(n-1)$

We plug in $t_1 = 5 \text{ and } d = -3$ and simplify

$t_n = t_1+d(n-1)\\t_n = 5+(-3)(n-1)\\t_n = 5-3n+3\\t_n = -3n+8$

Then we can plug in various positive whole numbers for n to find the corresponding $t_n$ value. For example, plug in n = 2

$t_n = -3n+8\\t_2 = -3*2+8\\t_2 = -6+8\\t_2 = 2$

which matches with the second term we found earlier. And,

$tn = -3n+8\\t_{10} = -3*10+8\\t_{10} = -30+8\\t_{10} = \boldsymbol{-22} \ \textbf{ is the tenth term}$

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The notation $S_{10}$ refers to the sum of the first ten terms $t_1, t_2, \ldots, t_9, t_{10}$

We could use either the long way or the shortcut above to find all $t_1$ through $t_{10}$ . Then add those values up. Or we can take this shortcut below.

$Sn = \text{sum of the first n terms of an arithmetic sequence}\\S_n = (n/2)*(t_1+t_n)\\S_{10} = (10/2)*(t_1+t_{10})\\S_{10} = (10/2)*(5-22)\\S_{10} = 5*(-17)\\\boldsymbol{S_{10} = -85}$

The sum of the first ten terms is -85

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As a check for $S_{10}$ , here are the first ten terms:

t1 = 5
t2 = 2
t3 = -1
t4 = -4
t5 = -7
t6 = -10
t7 = -13
t8 = -16
t9 = -19
t10 = -22

Then adding said terms gets us...

5 + 2 + (-1) + (-4) + (-7) + (-10) + (-13) + (-16) + (-19) + (-22) = -85

This confirms that $S_{10} = -85$ is correct.

6 0

2 years ago

Which of the following could be used to calculate the area of a sector in the circle shown below

lara [203]

Answer:

Therefore the Last option is correct

$\textrm{Area of Sector ACD}=\pi (8\ in)^{2}\times (\frac{42}{360})$

Step-by-step explanation:

Given:

Radius = r = 8 in

θ = 42°

To Find:

Area of Sector = ?

Solution:

We know that

$\textrm{Area of Sector}=\pi (Radius)^{2}\times \frac{\theta}{360}$

Substituting the given values in the formula we get

$\textrm{Area of Sector ACD}=\pi (8\ in)^{2}\times (\frac{42}{360})$

Which is the required Answer.

Therefore the Last option is correct

$\textrm{Area of Sector ACD}=\pi (8\ in)^{2}\times (\frac{42}{360})$

8 0

3 years ago

In the last 40 days, Mr. Neptune's newspaper has been delivered late 6 times. What is the experimental probability that it will

WINSTONCH [101]

Answer:

Step-by-step explanation:

The reason for this is simply because if you take 40 and 6, turn it into a fraction, then turn it into a percentage, it turns out to be 15%

3 0

2 years ago

What would the amplitude be? How do I find it? Should I add 1.25+6.75 then divide by 2 ?

Elis [28]

Answer:

2.75

Step-by-step explanation:

The amplitude is half of the difference between the highest and lowest y-coordinates.

amplitude = 0.5|6.75 - 1.25| = 0.5(5.5) = 2.75

3 0

3 years ago

223x12 please tell me I'm in my last question and dieing.

svlad2 [7]

Answer:

2,676

Step-by-step explanation:

2,676=223x12

7 0

2 years ago