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3 years ago

Find the sum of a finite geometric sequence from n=1 to n=8, using the expression -2(3)^n-1

1 answer:

8 0

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}
\end{cases}
\\\\\\
\sum\limits_{n=1}^{8}~-2(3)^{n-1}~~
\begin{cases}
n=8\\
a_1=-2\\
r=3
\end{cases}\implies S_8=-2\left( \cfrac{1-3^8}{1-3} \right)
\\\\\\
S_8=\underline{-2}\left( \cfrac{1-6561}{\underline{-2}} \right)\implies s_8=1-6561\implies S_8=-6560$

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9/20

Stella [2.4K]

Question:

Find the number of real number solutions for the equation. x^2 + 5x + 7 = 0

Answer:

The number of real solutions for the equation $x^{2}+5 x+7=0$ is zero

Solution:

For a Quadratic Equation of form : $a x^{2}+b x+c=0$ ---- eqn 1

The solution is $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Now , the given Quadratic Equation is $x^{2}+5 x+7=0$ ---- eqn 2

On comparing Equation (1) and Equation(2), we get

a = 1 , b = 5 and c = 7

In $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ , $b^2 - 4ac$ is called the discriminant of the quadratic equation

Its value determines the nature of roots

Now, here are the rules with discriminants:

1) D > 0; there are 2 real solutions in the equation

2) D = 0; there is 1 real solution in the equation

3) D < 0; there are no real solutions in the equation

Now let solve for given equation

$D= b^2 - 4ac\\\\D = 5^2 - 4(1)(7)\\\\D = 25 - 28 \\\\D = -3$

Since -3 is less than 0, this means that there are 0 real solutions in this equation.

4 0

3 years ago

Find all values of x such that sin 2x = sin x and 0 ≤ x ≤ 2π.

jarptica [38.1K]

Hello :
 sin 2x = sin x and 0 ≤ x ≤ 2π.
all solutions :
2x= x +2kπ or x= π -x +2kπ ..... k in : Z
x = 2kπ or : x = π/2 + kπ
but :
0 ≤ x ≤ 2π
all values of x such that sin 2x = sin x and 0 ≤ x ≤ 2π are :
k = 0 : x=0 , x= π/2
k=1 : x=2 π , x=3π/2

5 0

2 years ago

Write the verbal sentence as an equation:

-Dominant- [34]

Answer:

2n-12=7n-15

Step-by-step explanation:

I hope i did it right im sorry if i didnt! in the first sentence it tells you "twelve less than" therefore its telling you that you are going to be subtracting which automatically means that its not going to be the first thing you write down. You then continue reading and it tells you "2 times a number (n)" which is written as 2n because to things side by side like that signifies that you are multiplying. Then you have your equal sign which is self explanatory. and basically you follow the same reasoning as you did the first part and you end up with 7n-15 and the other half of your equation. I hope that helped!

4 0

3 years ago

I NEED HELP PRONTO PLZZZ HELP ME

forsale [732]

Answer:

12 ÷ 4

Step-by-step explanation:

Let's try to solve the given expression to see if it matches with any of the options guven..

$\frac{1}{4}*12$

$= \frac{1*12}{4}$

$= \frac{12}{4}$ (this is equivalent to 12 ÷ 4, which is given in the question)

Thus,

12 ÷ 4 equivalent to $\frac{1}{4}*12$

4 0

3 years ago

Which statement is best supported by the dot plot? Choose ONE and explain your

natima [27]

Answer:

The first statement.

Step-by-step explanation:

Because when you look at the July graph you can see that the highest number of miles is 15 and the lowest number of miles is 1 so the range is 15 - 1 = 14.

When you look at the August graph you can see that the highest number of miles is 13 and the lowest number of miles is 5 so the range is 13 - 5 = 8

So the range of the July month is greater than the range of the August month

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2 years ago