All categories

3 years ago

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:

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

A square pyramid has a base with side lengths each measuring 40 inches. The pyramid is 21 inches tall, with a slant height of 29

Alchen [17]

Answer

Find out the what is the surface area of the pyramid .

To proof

Formula

Surface area of a square pyramid

$= a^{2} + 2a \sqrt{\frac{a^{2}}{4} +h^{2}$

Where a is the base edge and h be the height .

As given

A square pyramid has a base with side lengths each measuring 40 inches. The pyramid is 21 inches tall, with a slant height of 29 inches.

i.e Base edge = 40 inches

Height = 21 inches

Put values in the above formula

$= 40^{2} + 2\times40\times\sqrt{\frac{40^{2}}{4} +21^{2}$

solving

$= 1600 + 80 \sqrt{\frac{1600}{4} + 441$

$= 1600 + 80\times\sqrt{841}$

$\sqrt{841} = 29$

= 1600 + 80 × 29

= 3920 inches²

Therefore the surface area of the pyramid is 3,920 inches²

Hence proved

4 0

3 years ago

Read 2 more answers

The weather forecast for the weekend is a 34% chance of rain for Saturday and a 32% chance of rain for Sunday. If we assume that

kaheart [24]

Answer:

$P( A \cap B) = P(A) *P(B) = 0.34*0.32 = 0.1088$

And then replacing in the total probability formula we got:

$P(A \cup B) = 0.34+0.32 - 0.1088 = 0.5512$

And rounded we got $P(A \cup B ) = 0.551$

That represent the probability that it rains over the weekend (either Saturday or Sunday)

Step-by-step explanation:

We can define the following notaton for the events:

A = It rains over the Saturday

B = It rains over the Sunday

We have the probabilities for these two events given:

$P(A) = 0.34 , P(B) = 0.32$

And we are interested on the probability that it rains over the weekend (either Saturday or Sunday), so we want to find this probability:

$P(A \cup B)$

And for this case we can use the total probability rule given by:

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

And since we are assuming the events independent we can find the probability of intersection like this:

$P( A \cap B) = P(A) *P(B) = 0.34*0.32 = 0.1088$

And then replacing in the total probability formula we got:

$P(A \cup B) = 0.34+0.32 - 0.1088 = 0.5512$

And rounded we got $P(A \cup B ) = 0.551$

That represent the probability that it rains over the weekend (either Saturday or Sunday)

6 0

3 years ago

The supplement of an angle is four times the complement of the angle find the measure of the complement

Morgarella [4.7K]

Answer:

The measure of the complement is 30°

Step-by-step explanation:

we know that

Two angles are supplementary if their sum is equal to 180 degrees

Two angles are complementary if their sum is equal to 90 degrees

Let

x -----> the measure of an angle

we know that

180°-x=4(90°-x)

Solve for x

180°-x=360°-4x

4x-x=360°-180°

3x=180°

x=60°

Find the complement

90°-x=90°-60°=30°

8 0

3 years ago

Read 2 more answers

Answer this question to get marked as brainliest!!!!

Mazyrski [523]

Answer: C

Step-by-step explanation:

A= 1/2(a+b)xh

A=1/2(7+10)x5

A=8.5x5

A=42.5

4 0

3 years ago

You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? 2x - 3y = 12

suter [353]

Answer:

Step-by-step explanation:

The Elimination Method is the method for solving a pair of linear equations which reduces one equation to one that has only a single variable.

If the coefficients of one variable are opposites, you add the equations to eliminate a variable, and then solve.

If the coefficients are not opposites, then we multiply one or both equations by a number to create opposite coefficients, and then add the equations to eliminate a variable and solve.

When multiplying the equation by a coefficient, we multiply both sides of the equation (multiplying both sides of the equation by some nonzero number does not change the solution).

So, option B is not allowed (it is not allowed to multiply only one part of the equation)

6 0

3 years ago