Help plzz hurry i didnt study and need help

Find the sixth term of the sequence 1/2, -3/8, 9/32

sukhopar [10]

Answer:

The sixth term is -243/2048 ⇒ answer B

Step-by-step explanation:

* Lets explain the geometric sequence

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)

# 5000 , 1000 , 200 , 40 , …………………………(÷5)

* General term (nth term) of a Geometric sequence:

# U1 = a , U2 = ar , U3 = ar² , U4 = ar³ , U5 = ar^4

# Un = ar^(n-1), where a is the first term , r is the constant ratio

between each two consecutive terms and n is the position of the

number in the sequence

- Ex: U5 = ar^4 , U7 = ar^6 , U10 = ar^9 , U12 = ar^11

- Lets solve the problem

∵ The sequence is 1/2 , -3/8 , 9/32

- Lets find the constant ratio r

∵ The first term is a = 1/2

∵ The second term is U2 = ar

∵ The second term U2 = -3/8

∴ ar = -3/8

∴ 1/2 r = -3/8 ⇒ multiply both sides by 2

∴ r = -3/4

- Lets find the sixth term

∵ a = 1/2 and r = -3/4

∵ n = 6

∴ U6 = ar^5

∴ U6 = 1/2 (-3/4)^5 = 1/2 × -243/1024 = -243/2048

* The sixth term is -243/2048

8 0

3 years ago

Read 2 more answers

Calls to a customer service center last on average 1.4 minutes with a standard deviation of 1.7 minutes. An operator in the call

igomit [66]

Answer:

the expected total amount of time in minutes is 88.4

Step-by-step explanation:

The computation of the expected total amount of time in minutes is given below:

= Standard deviation × needed to answer calls each day

= 1.7 × 52

= 88.4

hence, the expected total amount of time in minutes is 88.4

8 0

2 years ago

Evaluate the expression for a = 4 and b = 3. A-81 B-24 C-36 D-144

Dimas [21]

Where the expression....

4 0

3 years ago

How many solutions are in 6-2(3-2x)=-4(3-x) ?

Daniel [21]

Answer:

Step-by-step explanation:

there is no solution:

6-2(3-2x) = -4(3-x)

6-6+4x= -12+4x

4x= -12+4x

0=-12

4 0

2 years ago

Read 2 more answers

The diagram below shows a square inside a regular octagon. The apothem of the octagon is 15.69 units. To the nearest square unit

Musya8 [376]

Answer:

C. 647 square units

Step-by-step explanation:

To find the shaded area, subtract the area of the unshaded square from the area of the octagon.

Area of the octagon

$\textsf{Area of a regular polygon}=\dfrac{n\:l\:a}{2}$

where:

n = number of sides
l = length of one side
a = apothem

Given:

n = 8
l = 13
a = 15.69

Substitute the given values into the formula and solve for A:

$\implies \textsf{Area}=\sf \dfrac{8 \cdot 13 \cdot 15.69}{2}$

$\implies \textsf{Area}=\sf \dfrac{1631.76}{2}$

$\implies \textsf{Area}=\sf 815.88\:\:square \:units$

Area of the square

$\implies \textsf{Area}=\sf 13^2=169 \:\:square \:units$

Area of the shaded region

= area of the octagon - area of the square

= 815.88 - 169

= 646.88

= 647 square units (nearest square unit)

3 0

2 years ago

Read 2 more answers