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Molodets [167]
3 years ago
15

the second term of a geometric sequence is 18 and the fourth term is 8 find the common ratio . And find the sum of the first 6 t

erms
Mathematics
1 answer:
777dan777 [17]3 years ago
8 0

Answer:

  • ratio: 2/3
  • sum: 73 8/9

Step-by-step explanation:

The general term of a geometric sequence is ...

  an = a1·r^(n-1)

You have the 2nd and 4th terms, so ...

  a2 = a1·r^(2-1) = a1·r

  a4 = a1·r^(4-1) = a1·r^3

We can find r from the ratio ...

  a4/a2 = (a1·r^3)/(a1·r) = r^2 = 8/18 = 4/9

Then r is ...

  r = √(4/9) = 2/3 . . . . the common ratio

The first term is ...

  a2 = 18 = a1·(2/3)

  a1 = (3/2)·18 = 27

__

The sum of the first 6 terms is ...

  Sn = a1·(r^n -1)/(r -1)

  S6 = 27·((2/3)^6 -1)/(2/3 -1)

  S6 = 27·(64/729-1)/(2/3-1) = (27)(665)/243 = 73 8/9

The sum of the first 6 terms is 73 8/9.

_____

<em>Check on the sum</em>

The first 6 terms are ...

  27, 18, 12, 8, 5 1/3, 3 5/9

Their sum is 73 8/9, as above.

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Two divers are swimming at different depths below sea level. One diver is at -25.5 ft. The other diver is at -40.75 ft. How far
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Answer:

66.25 ft

Step-by-step explanation:

25.5 + 40.75

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3 years ago
The ratio of cassette to compact disc is 10 to 3 and the number of cassettes is 10 less than 5 times the number of compact discs
OlgaM077 [116]

There are 20 cassettes.

Step-by-step explanation:

Given,

Ratio of cassette to compact disc = 10:3

Let,

the number of cassettes = 10x

Number of compact disc = 3x

According to given statement;

the number of cassettes is 10 less than 5 times the number of compact discs.

10x = 5(Number of CD) - 10

10x=3(5x)-10 \\10x=15x-10\\10=15x-10x\\10=5x\\5x=10

Dividing both sides by 5

\frac{5x}{5}=\frac{10}{5}\\x=2

Number of cassettes= 10x = 10(2) = 20

There are 20 cassettes.

Keywords: variable, ratio

Learn more about variables at:

  • brainly.com/question/10414011
  • brainly.com/question/10483199

#LearnwithBrainly

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