Determine 6th term in the geometric sequence whose first term is 3 and whose common ratio is -4.

Answers

Answer 1

Answer: $a_1=3$
$a_2=-4a_1$
$a_3=-4a_2=(-4)^2a_1$
$\cdots$
$a_6=-4a_5=\cdots=(-4)^5a_1$

$\implies a_6=(-4)^5\cdot3=-3072$

Related Questions

How do you solve this
You and a friend both leave the same restaurant to drive home. You are heading directly west at 30 miles per hour and he or she is heading directly south at 40 miles per hour. After half an hour, how fast (in mph) is the distance between you changing? Do not include units in your answer.
What is the sum of the polynomials?(8x^2 - 9y^2 - 4x) + (x^2 - 3y^2 - 7x) * 7x^2 - 6y^2 + 3x * 9x^2 - 6y^2 + 3x * 9x^2 - 12y^2 + 3x * 9x^2 - 12y^2 - 11x
The ratio of cats to dogs at the shelter is 3 to 2 if there are 15 cats at the shelter how many dogs are there
Jessie owns a hot dog stand and sells specialized hot dogs. He charges $1.50 for a plain hot dog and then an additional $0.50 for each topping that you want. This can be modeled by the equation C = .5x + 1.5, where C is the total cost of the hot dog and x is the number of toppings you ordered. The company that he buys his hot dogs from was having a sale so he was able to buy the hot dogs for less. He will now sell them for $0.25 less than before. What should be changed in the equation C = .5x + 1.5 to represent this?

You decide to play roulette 4 times, each time betting on red. What is the distribution of X, the number of times you win?

Answers

Using the concept of binomial probability, the distribution of X which is the number of winning is ;

X ______ 0 ____1 _____ 2___ 3______ 4

P(X):_0.0767_0.2762_0.3729_0.2238_0.0503

Given the parmaters :

Total Number of slots = 38
Number of reds = 18

The probability of winning,p on a single play :

p = (red slots / total slots) = 18/38 = 9/19

Number of plays = 4

Number of winnings = X

Using the binomial probability relation :

P(x = x) = nCx * p^x * q^(n-x)
q = 1 - 9/19 = 10/19
n = 4

ForX=0:

P(x = 0) = 4C0 × (9/19)^0 × (10/19)⁴ = 0.0767

ForX=1:

P(x = 0) = 4C1 × (9/19)¹ × (10/19)³ = 0.2762

ForX=2:

P(x = 2) = 4C2 × (9/19)² × (10/19)² = 0.3729

ForX=3:

P(x = 3) = 4C3 × (9/19)³ × (10/19)¹ = 0.2238

For X = 4 :

P(x = 4) = 4C4 × (9/19)⁴ × (10/19)^0 = 0.0503

Therefore, the distribution of X in the roulette spin is :

X ____ 0 ____ 1 _____ 2 ______ 3 ______ 4

P(X):_0.0767_0.2762_0.3729_0.2238 _0.0503

Learn more :brainly.com/question/12474772

1.
If betting on red, 18/38 = 9/19 chance of winning, so 10/19 chance of losing
Chance of winning 4 times: (9/19)^4 = 6561/130321 =~ 5.034%
Chance of winning 3 times: (9/19)^3 * (10/19) * C(4,1) = 29160/130321 =~ 22.3755%
Chance of winning 2 times: (9/19)^2 * (10/19)^2 * C(4,2) = 48600/130321 =~ 37.2925%
Chance of winning 1 time: (9/19) * (10/19)^3 * C(4,3) = 36000/130321 =~ 27.624%
Chance of winning 0 times: (10/39)^4 = 10000/130321 =~ 76.7336%

What is the remainder when you divide
(2x^3– 5x – 7) by (x + 2) ?

Answers

Answer:

this is the remainder.

Final answer:

To find the remainder, use polynomial long division to divide (2x^3 - 5x - 7) by (x + 2).

Explanation:

To find the remainder when dividing (2x^3 - 5x - 7) by (x + 2), we can use polynomial long division. First, divide the first term of the numerator by the first term of the divisor to get the quotient. Multiply the divisor by the quotient and subtract it from the numerator. Repeat this process until you have subtracted all terms of the divisor from the numerator. The resulting polynomial after division will be the remainder. In this case, the remainder will be 17x - 31.