Please help me on this!!

Write the first five terms of the sequence defined by the recursive formula

stepan [7]

Answer:

The correct answer option is: $S_9=\frac{9}{2} (2+26)$

Step-by-step explanation:

We know that,

the sum of the first $n$ terms of an Arithmetic Sequence is given by:

$S_9=\frac{n(a_1+a_n)}{2}$

where $n$ is the number of terms,

$a_1$ is the first term of the sequence; and

$a_n$ is the first term of the sequence.

So for $a_n=3n-1$ ,

$a_1=3(1)-1=2$

and

$a_9=3(9)-1=26$

Putting these values in the formula to get:

$S_9=\frac{9(a_1+a_9)}{2}$

$S_9=\frac{9(2+26)}{2} \\\\S_9=\frac{9}{2} (2+26)$

First five terms:

$a_1=3(1)-1=2$

$S_1=\frac{1(2+2)}{2}$ =2

$a_2=3(2)-1=5$

$S_2=\frac{2(2+5)}{2}$ =7

$a_3=3(3)-1=8$

$S_2=\frac{3(2+8)}{2}$ =15

$a_4=3(4)-1=11$

$S_4=\frac{4(2+11)}{2}$ =26

$a_5=3(5)-1=14$

$S_5=\frac{5(2+14)}{2}$ =40

8 0

2 years ago

Read 2 more answers

What are the center and radius of the circle defined by the equation x^2 + y^2 -6x + 4y + 4=0

Sloan [31]

The equation of a circle:

$(x-h)^2+(y-k)^2=r^2$

(h, k) - a coordinates of the center

r - a radius

$x^2+y^2-6x+4y+4=0\ \ \ |-4\\\\x^2-2\cdot x\cdot3+y^2+2\cdot y\cdot2=-4\ \ \ |+3^2\ |+2^2\\\\\underbrace{x^2-2\cdot x\cdot3+3^2}_{(a-b)^2=a^2-2ab+b^2}+\underbrace{y^2+2\cdot y\cdot2+2^2}_{(a+b)^2=a^2+2ab+b^2}=-4+3^2+2^2\\\\(x-3)^2+(y+2)^2=3^2$

Answer:

the center: (3, -2)

the radius: 3

5 0

2 years ago

Cardiovascular disease is a major cause of death and illness worldwide, with high blood pressure and high LDL cholesterol both b

valkas [14]

Answer:

Null and alternative hypotheses:

H0: p1 = p2

H1: p1 ≠ p2

To find the sample proportions, we have the following:

$p'1 = \frac{x_1}{n_1} = \frac{113}{3180} = 0.0355$

$p'2 = \frac{x_2}{n_2} = \frac{157}{3168} = 0.0495$

$p' = \frac{(x_1 + x_2}{n_1 + n_2} = \frac{113 + 157}{3180 + 3168} = 0.0425$

Calculate Z statistics:

$z = \frac{(p1 -p2)}{\sqrt{(p'(1-p')*(\frac{1}{n1}+ \frac{1}{n2})}}$

$= \frac{(0.0355 - 0.0495)}{\sqrt{(0.0425*(1-0.0425) * (\frac{1}{3180} + \frac{1}{3168})}} = -2.764$

Z = -2.764

P-value = 0.00285

The pvalue is low.

Since the pvalue is low, reject null hypothesis, H0.

Conclusion:

There is strong evidence that patients experiencing the primary outcome is different for those receiving the treatment compared to those without

7 0

2 years ago

7y + 2x − 10y + 3x2 − 10x

Anni [7]

Answer:

3x^2-8x-3y

Step-by-step explanation:

combine like turms and rearrange

5 0

1 year ago

How do I solve this equation????

Alexus [3.1K]

So for this question (for finding x and y) you will want to use elimination. To do this you will need to bring the x and y to the same side (I put them on the left):
-3/2x+y=6
x+y=0
Now subtract the y on the bottom from the top to isolate x:
3/2x=6
Now the easiest way to bring over the 3/2 to isolate the x fully is to convert it to decimal (1.5) and divide it by 6 (because when multiplication on one side of problem the only way to bring it over is to divide):
x=6/1.5
which simplifies to:
x=4
Hope this helps!

4 0

2 years ago