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Aliun [14]
3 years ago
12

Which formula can be used to find the nth term of a geometric sequence where the fifth term is 1/6 and the common ratio is 1/4?

Mathematics
1 answer:
OlgaM077 [116]3 years ago
3 0

Answer:

a_n = 16(\frac{1}{4})^{n - 1}

Step-by-step explanation:

Given:

Fifth term of a geometric sequence = \frac{1}{16}

Common ratio (r) = ¼

Required:

Formula for the nth term of the geometric sequence

Solution:

Step 1: find the first term of the sequence

Formula for nth term of a geometric sequence = ar^{n - 1}, where:

a = first term

r = common ratio = ¼

Thus, we are given the 5th term to be ¹/16, so n here = 5.

Input all these values into the formula to find a, the first term.

\frac{1}{16} = a*\frac{1}{4}^{5 - 1}

\frac{1}{16} = a*\frac{1}{4}^{4}

\frac{1}{16} = a*\frac{1}{256}

\frac{1}{16} = \frac{a}{256}

Cross multiply

1*256 = a*16

Divide both sides by 16

\frac{256}{16} = \frac{16a}{16}

16 = a

a = 16

Step 2: input the value of a and r to find the nth term formula of the sequence

nth term = ar^{n - 1}

nth term = 16*\frac{1}{4}^{n - 1}

a_n = 16(\frac{1}{4})^{n - 1}

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The position of an object moving along an x axis is given by x = 3.24 t - 4.20 t2 + 1.07 t3, where x is in meters and t in secon
Pavel [41]

Answer and explanation:

Given : The position of an object moving along an x axis is given by x=3.24t-4.20t^2+1.07t^3 where x is in meters and t in seconds.

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a) At t= 1 s

x(t)=3.24t-4.20t^2+1.07t^3

x(1)=3.24(1)-4.20(1)^2+1.07(1)^3

x(1)=3.24-4.20+1.07

x(1)=0.11

b) At t= 2 s

x(t)=3.24t-4.20t^2+1.07t^3

x(2)=3.24(2)-4.20(2)^2+1.07(2)^3

x(2)=6.48-16.8+8.56

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c) At t= 3 s

x(t)=3.24t-4.20t^2+1.07t^3

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x(3)=0.81

d) At t= 4 s

x(t)=3.24t-4.20t^2+1.07t^3

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x(4)=12.96-67.2+68.48

x(4)=14.24

(e) What is the object's displacement between t = 0 and t = 4 s?

At t=0, x(0)=0

At t=4, x(4)=14.24

The displacement is given by,

\triangle x=x(4)-x(0)

\triangle x=14.24-0

\triangle x=14.24

(f) What is its average velocity from t = 2 s to t = 4 s?

At t=2, x(2)=-1.76

At t=4, x(4)=14.24

The average velocity  is given by,

\triangle x=x(4)-x(2)

\triangle x=14.24-(-1.76)

\triangle x=14.24+1.76

\triangle x=16

4 0
3 years ago
Someone please help me
Katarina [22]
Its the same shape so it would be A.
and C because they are similar
5 0
3 years ago
Angle TVZ makes a linear pair with angle ZVW so the measure of angle TVZ plus the measure of angle ZVW=180 degrees. Angle ZVW is
ss7ja [257]

Answer:

Step-by-step explanation:

2x +15 +2x +5 = 180

4x = 180 - 20

x = 160/4

x = 40

TVZ + 2x +5 =180

TVX +2(40) = 180 -5

TVX = 175 - 80

TVX = 95

6 0
3 years ago
n the right triangular prism below, BG FC The volume of the prism is 900 cubic centimeters. The height of the prism is 15 centim
Bad White [126]
12 cm

Remember, V=Bh

-I think I did the process incorrectly but this is what I did:
900=(10)(15)
900=150 (divide 150 on both sides)
you get 6 but then I multiplied by 2 and got 12.
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6 0
3 years ago
Read 2 more answers
Help please:) i will appreciate it a lot
katen-ka-za [31]

Answer:

Point c

Step-by-step explanation:

Hope this helps

5 0
3 years ago
Read 2 more answers
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