All categories

3 years ago

If f(1)=6f(1)=6 and f(n)=nf(n-1)-4f(n)=nf(n−1)−4 then find the value of f(3)f(3).

Mathematics

2 answers:

nekit [7.7K]3 years ago

8 0

Answer:6144

Step-by-step explanation:

If f(1)=6f(1)=6 and f(n)=4f(n-1)f(n)=4f(n−1) then find the value of f(6)f(6).

f(1)=

\,\,6

f(\color{darkgreen}{2})=

f(2)=

\,\,4f(\color{darkgreen}{2}-1)

4f(2−1)

\,\,4f(1)

4f(1)

\,\,4(6)

4(6)

Substitute f(1)=6

f(2)=

\,\,24

f(\color{darkgreen}{3})=

f(3)=

\,\,4f(\color{darkgreen}{3}-1)

4f(3−1)

\,\,4f(2)

4f(2)

\,\,4(24)

4(24)

Substitute f(2)=24

f(3)=

\,\,96

f(\color{darkgreen}{4})=

f(4)=

\,\,4f(\color{darkgreen}{4}-1)

4f(4−1)

\,\,4f(3)

4f(3)

\,\,4(96)

4(96)

Substitute f(3)=96

f(4)=

\,\,384

384

f(\color{darkgreen}{5})=

f(5)=

\,\,4f(\color{darkgreen}{5}-1)

4f(5−1)

\,\,4f(4)

4f(4)

\,\,4(384)

4(384)

Substitute f(4)=384

f(5)=

\,\,1536

1536

f(\color{darkgreen}{6})=

f(6)=

\,\,4f(\color{darkgreen}{6}-1)

4f(6−1)

\,\,4f(5)

4f(5)

\,\,4(1536)

4(1536)

Substitute f(5)=1536

f(6)=

\,\,6144

6144

\text{Geometric Sequence:}

Geometric Sequence:

Common ratio of 4

6,24,96,384,1536,6144, ...

6,24,96,384,1536,6144,...

\text{Final Answer:}

Final Answer:

6144

alekssr [168]3 years ago

6 0

Answer:

Step-by-step explanation:

You might be interested in

What is the area of this figure?

lesantik [10]

Answer:

$\Huge\boxed {A =859ft^{2} }$

Step-by-step explanation:

Hello There!

To solve for the area of this figure we need to split the figure into 3 different parts:

A rectangle with a length of 9 ft and a width of 7 ft

a rectangle with a width of 9ft + 7ft and a length of 25 ft

a rectangle with a width of 18 ft and a length of 22 ft

To find the area of a rectangle we use the formula

$A=w*l$ where w = width and l = length

for the first one we plug in the values

A = 9 * 7

9 * 7 = 63 so the area of the smallest rectangle is 63ft²

Now lets find the area of the larger rectangle

The dimensions are l = 25 ft and w = 9 + 7 (16 ft)

Now we can plug in the values into the area formula

A = 16 * 25

16*25=400 so the area of the larger rectangle is 400 ft²

Now lets find the area of the last rectangle

The dimensions are l = 22 ft and w = 18 ft

now lets plug in the values to the formula

A = 22 * 18 =396

so the area of the last rectangle is 396 ft²

Finally we want to add all of the areas together

396 + 400 + 63 = 859

So the area of the figure is 859 ft²

7 0

3 years ago

Read 2 more answers

Joseph gives a math test to all the students in a middle school and notices that taller students have higher scores. He conclude

MariettaO [177]

Answer:

D) justified, assuming that the test was given fairly

7 0

3 years ago

Please help

lubasha [3.4K]

Let us check series : -10 /-2 = 5 -50/-10 = 5

so it is a geometric series with a= -2 and r= 5

sum formula for n terms of geometric series = a ( r^n -1 ) /( r-1)

here we find S5 that is n= 5 = -2 ( 5^ 5 - 1) /( 5-1)

= -2 ( 3125 -1) / 4 = -1562

second series is : 1.5/1 = 1.5 2.25/1.5 = 1.5

this is also geometric series but n = 12 a= 1 and r= 1.5

we use same formula

S12 = 1 ( (1.5) ^12 -1) /( 1.5-1) =

128.74 / 0.5 = 257.49

Last is 2/1= 2 4/2 = 2 8/4 = 2 so r = 2 a = 1 and n = 12

we use same formula 1 ( 2^12 - 1) / (2-1)

= 4095

Answers : -1562 , 257.49 , 4095

8 0

3 years ago

Read 2 more answers

1.The following points (-4, -5), (-1, -5), (0, -5), (4, -5) are drawn on a coordinate plain. What is the domain of this function

Nutka1998 [239]

Answer:

1). (B) ; 2). (A) ; 3). (C)

Step-by-step explanation:

1). { - 4, - 1, 0, 4 }

2). { - 5 }

3). m = 0

6 0

3 years ago

Find the value of x.

konstantin123 [22]

Answer:

x= 37.5°

Step-by-step explanation:

∠CBD

= 180° -75° (adj. ∠s on a str. line)

= 105°

∠BCD= ∠BDC (base ∠s of isos. △BCD)

∠BCD= x

∠BCD +∠BDC +∠CBD= 180° (∠ sum of △BCD)

x +x +105°= 180°

2x= 180° -105°

2x= 75°

x= 37.5°

Alternative working:

∠BDA= (180° -75°) ÷2 (base ∠s of isos. △ABD)

∠BDA= 52.5°

∠BDA +∠BDC= 90°

52.5° +x= 90°

x= 90° -52.5°

x= 37.5°

6 0

3 years ago