I want to know the answer of the question on the top

Find the 12th term of the geometric sequence 5, -25, 125, ...5,−25,125,...

katovenus [111]

Answer:

$a_{12}=-244140625$

Step-by-step explanation:

Considering the geometric sequence

$5,-25,\:125,\:...$

$a_1=5$

As the common ratio ' $r$ ' between consecutive terms is constant.

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}$

$r=\frac{-25}{5}=-5$

$r=\frac{125}{-25}=-5$

The general term of a geometric sequence is given by the formula:

$a_n=a_1\cdot \:r^{n-1}$

where $a_1$ is the initial term and $r$ the common ratio.

Putting $n = 12$ , $r = -5$ and $a_1=5$ in the general term of a geometric sequence to determine the 12th term of the sequence.

$a_n=a_1\cdot \:r^{n-1}$

$a_n=5\left(-5\right)^{n-1}$

$a_{12}=5\left(-5\right)^{12-1}$

$=5\left(-5^{11}\right)$

$\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a$

$=-5\cdot \:5^{11}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}$

$=-5^{1+11}$ ∵ $5\cdot \:5^{11}=\:5^{1+11}$

$=-244140625$

Therefore,

$a_{12}=-244140625$

6 0

2 years ago

Divid 15 into two parts such that the sum of their reciprocal is 3/10

emmasim [6.3K]

Let x and y be the 2 parts of 15 ==> x + y=15 (given)

Reciprocal of x and y ==> 1/x +1/y ==> 1/x + 1/y = 3/10 (given)

Let's solve 1/x + 1/y = 3/10 . Common denominator = 10.x.y (reduce to same denominator)

==> (10y+10x)/10xy = 3xy/10xy ==> 10x+10y =3xy

But x+y = 15 , then 10x+10y =150 ==> 150=3xy and xy = 50

Now we have the sum S of the 2 parts that is S = 15 and
their Product = xy =50
Let's use the quadratic equation for S and P==> X² -SX +P =0
Or X² - 15X + 50=0, Solve for X & you will find:
The 1st part of 15 is 10 & the 2nd part is 5

4 0

3 years ago

-. For each equation below, determine whether

Andre45 [30]

Answer:

Step-by-step explanation:

The first answer a, is not a linear function because of the first term, 2√(x), this is basically 2(x^(1/2)) which means that it is not linear

B is linear because there are no exponents in any of the variables.

C is not linear because it forms a circle when graphed

D is linear because there are no exponents in any of the variables.

E is linear because there are no exponents in angy of the variables.

F is linear because there are no exponents in any of the variables.

G is not linear because it is a quadratic equation.

7 0

2 years ago

Read 2 more answers

Is this triangle acute, right, or obtuse?

Elza [17]

Answer:

acute

Step-by-step explanation:

every angle is under 90 degrees

7 0

3 years ago

Read 2 more answers

Help me pls!!

tresset_1 [31]

(a) Truck carries 90 gallons of diesel fuel to 660 miles.

So, 1 gallon of diesel fuel to 660/90 = 22/3 miles.

30 gallons of diesel fuel to = 220 miles.

Hence, if x-axis represents the number of miles and y-axis represents the number of gallons, then, (660, 90) and (220, 30) are points on the graph.

Join (660, 90) and (220, 30), we get the graph of a line.

Note that (0, 0) is also a point on the line.

Equation of the line is .

(b) x represents the number of miles. Therefore, the possible values for x is the closed interval [0, 660].

Hence, the domain of the function is [0, 660].

(c) Origin represents that the truck is not moving and there is no diesel fuel loaded in the truck.

7 0

2 years ago