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photoshop1234 [79]
3 years ago
6

Identify the recursive formula for the following sequence. 8, 16, 32, 64, ...

Mathematics
1 answer:
Dominik [7]3 years ago
7 0

Answer:

The  recursive formula for the given sequence

                 t_{n}=  (2)^{n+2}

Step-by-step explanation:

<u><em>Explanation</em></u>:-

Given sequence is 8 , 16, 32, 64 ,.....

First term is   a = 8

common ratio   r = \frac{16}{8} =2

                       r = \frac{32}{16} =2

                      r = \frac{64}{32} =2   and so on..

Given sequence of the common ratio 'r' is equal

The n^{th} term of the sequence

                   t_{n} = a r^{n-1}

                   t_{n}= 8 (2)^{n-1}

                   t_{n}=  (2)^{(3+n-1)}

                  t_{n}=  (2)^{n+2}

This is  recursive formula for the given sequence

                 t_{n}=  (2)^{n+2}

<u><em>Verification</em></u>:-

           t_{n}=  (2)^{n+2}

put n=1   ⇒ t₁ = 8

put n=2   ⇒ t₂ = 16

put n=3   ⇒ t₃ = 32

put n=4   ⇒ t₄= 64    

and so on..

The sequence  8 ,16 , 32 , 64 ....

                 

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Solve the inequality: -6n - 12 &gt;= 3(-n + 12)
Verizon [17]

Answer:

-16 > n or n < -16

Step-by-step explanation:

First, we can write the inequality and distribute.

-6n-12 > 3(-n+12)

-6n-12 > -3n+36

Get rid of a variable first (it makes solving a lot easier). We can add 6n to both sides.

-6n-12 > -3n+36

<u>+6n          +6n</u>

-12 > 3n+36

Now, we can subtract 36 on both sides.

-12 > 3n+36

<u>-36         -36</u>

-48 > 3n

Divide by 3 on both sides.

-48 > 3n

<u>/3       /3</u>

-16 > n or (if it's easier) n < -16

Hope this helps!! Have a wonderful day C:

7 0
2 years ago
Solve for X pleas help
nydimaria [60]

Answer:

10.5 I think

Step-by-step explanation:

(1/2) *12 is 6

(1/2)*21 is 10.5

3 0
2 years ago
18 ≥ -2x <br> i cant solve this
Bumek [7]

Answer:

x\geq -9

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
The edge of a cube was found to be 30 cm with a possible error in measurement of 0.5 cm. Use differentials to estimate the maxim
IgorLugansk [536]

Answer:

for the volume a cube

Possible error = 1350cm³

Relative error = 0.05

Percentage error = 5%

For the surface area of a cube

Possible error = 180cm²

Relative error = 0.0333

Percentage error = 3.33%

Step-by-step explanation:

A cube is a three dimensional solid object with six (6) faces, twelve (12) edges and eight(8) vertices.

The volume of a cube = x³

Where x= length of the edge of a cube

X = 30cm 0.5cm

Differentiate V with respect to x (V = Volume of a cube)

dV/dx= 3 x²

dV= 3 x² . dx

dV = 3 × 30² × (0.5)

dV= 2700(0.5)

= 1350cm³

Maximum possible error = 1350cm³

Relative error = possible error /Volume

= dV/V

Recall that V = x³

V= (30)³

A = 27000cm³

Substitute the values for and V into the formula for Relative error

Relative error = 1350/27000

Relative error = 0.05

% error = Relative error × 100

= 0.05× 100

= 5%

Surface Area of a cube = 6x²

A = 6x²

Differentiate A with respect to x

dA/dx = 12x

dA/dx = 12x . dx

= 12 × 30 (0.5)

= 180cm²

Maximum possible error = 180cm²

Relative error = possible error / surface area

= dA/A

Recall that A = 6x²

A = 6(30)²

A = 5400cm²

Substitute the values for and A into the formula for Relative error

Relative error = 180/5400

Relative error = 0.0333(4 decimal place)

% error = Relative error × 100

= 0.0333 × 100

= 3.33%

8 0
3 years ago
Please answer this asap
Mandarinka [93]

Answer:

I think it's division property and x = 6

5 0
3 years ago
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