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3 years ago

What is the fifth term of the geometric sequence whose first three terms are 486, 162, and 54?

Mathematics

1 answer:

Scorpion4ik [409]3 years ago

3 0

Answer:

Step-by-step explanation:

an = ar^(n-1)

a = first term

n = nth term

r = common ratio

r = r2 / r1 = r3 / r2

The first 3 terms are :

486, 162, and 54

Hence,

a = 486

r = 162 / 486 = 1/3

Hence ;

a5 = 486(1/3)^5 - 1

a5 = 486(1/3)^4

a5 = 486(1 / 81)

a5 = 486 * 1 / 81

a5 = 486 / 81

a5 = 6

The 5th term of the geometric progression will be ; 6

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Answer:

Part 6)

case a) $P(odd)=\frac{1}{2}=0.5=50\%$

case b) $P(less\ than\ 3)=\frac{0}{8}=0=0\%$

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case a) $P(yellow)=\frac{3}{20}=0.15=15\%$

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Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.

The size of the sample space is the total number of possible outcomes

The event space is the number of outcomes in the event you are interested in.

Let

x------> size of the event space

y-----> size of the sample space

$P=\frac{x}{y}$

Part 6)

case a) P(odd)

In this problem we have

$x=4$

$y=8$

substitute

$P=\frac{4}{8}=\frac{1}{2}=0.5=50\%$

case b) P (less than 3)

In this problem we have

$x=0$

$y=8$

substitute

$P=\frac{0}{8}=0=0\%$

Part 7)

case a) P(yellow)

In this problem we have

$x=3$

$y=20$

substitute

$P=\frac{3}{20}=0.15=15\%$

case b) P(green and red)

$P(green)=\frac{5}{20}$

$P(red)=\frac{4}{20}$

therefore

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3 years ago