Ask question

Ask question

All categories

2 years ago

5

What is the general term equation, a_n , for the arithmetic sequence 5, 1,–3, –7…and what is the 21st term of this sequence?

1 answer:

Aleksandr [31]2 years ago

4 0

The difference between each term is -4, so we know that part of the general term is -4n. Now we need to adjust -4n so at u1 it is 5. Therefore -4+x=5 and we rearrange to see x is 9.

Therefore our general sequence is:
$\boxed{u_n=-4n+9}$

Now we can substitute easily into the second equation with the common difference of 4:
$u_n=u_1+(n-1)d \\ u_{21}=5+(21-1)*-4 = 5-80 \\ \boxed{u_{21}=-75}$

You might be interested in

Find the measure of the missing angle.

Leya [2.2K]

Answer:

163

Step-by-step explanation:

inside of the pentagon it adds up to 540 degrees so u add all those angles together and take it away from 540

3 0

2 years ago

The vertices of PQRS have coordinates P(–1,5) , Q(3,4) , R(2,−4) , and S(−3,−2) .

aleksandrvk [35]

Answer:

P(5,1), Q(4,-3), R(-4,-2), S(-2,3)

Let me know if it’s correct !!

8 0

2 years ago

A roulette wheel has 38 3838 slots, of which 18 1818 are red, 18 1818 are black, and 2 22 are green. In each round of the game,

Elina [12.6K]

The value of P(R = 3) is 0.2854

<h3>Probability</h3>

Probabilities are used to determine the chances of events.

The given parameters are:

$n = 38$ --- the number of slots
$red = 18$ . --- the number of red slot
$black = 18$ . --- the number of black slot
$green = 2$ . --- the number of green slot

<h3>Individual probabilities</h3>

The probability that the ball lands on a red slot is calculated as:

$p = \frac{18}{38}$

Simplify

$p= \frac{9}{19}$

The probability that the ball does not land on a red slot is calculated as:

$q = \frac{18+2}{38}$

$q = \frac{20}{38}$

Simplify

$q = \frac{10}{19}$

<h3>Binomial probability</h3>

The value of P(R = 3) is then calculated using the following binomial probability formula

$P(R = r) = ^nC_rp^rq^{n-r}$

Where:

$n = 7$

$r = 3$

So, we have:

$P(R = 3) = ^7C_3 \times (9/19)^3 \times (10/19)^{7-3}$

$P(R = 3) = 35 \times (9/19)^3 \times (10/19)^4$

$P(R = 3) = 0.2854$

Hence, the value of P(R = 3) is 0.2854

Read more about probabilities at:

brainly.com/question/15246027

8 0

2 years ago

Read 2 more answers

Interpret the following Sigma Notation<br> n=152n

lora16 [44]

Okay so basically the answer would be
-8305
And in this form it would be
-151 + -302 + -435 -604 -755 + -906 + 1057 +-1208 + -1359 + 1510

8 0

2 years ago

Pls answer fast pls pls

forsale [732]

<h3><u>Answer</u> :- </h3>

c) 0.01

<h3><u>Solution</u> :-</h3>

To Write percentage in decimal or fraction we divide it by 100

therefore,

$\begin{gathered}\\\implies\quad \sf 2\% = \frac{2}{100} \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf 2\% = 0.02 \\\end{gathered}$

Half of 0.02 = $\sf\frac{1}{\cancel2} \times\cancel{0.02}$

$\implies\boxed {0.01}$

5 0

2 years ago

Read 2 more answers