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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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Answer:

2y - 25 = 19

2y = 19 + 25

2y = 44

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y = 22

Hope it helps

4 0
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Find highest common factor 12 &amp; 20
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5 0
3 years ago
Plz help me plzzzzz asap
Varvara68 [4.7K]

Answer:

2 \frac{2}{9}

Step-by-step explanation:

First, we will turn 5 2/5 into an improper fraction:

5 * 5 = 25 + 2 = 27/5

So they worked for 27/5 days.

We want to divide the days worked by the distance to get the unit rate of distance per day:

\frac{12}{\frac{27}{5} } = \frac{12}{1} * \frac{5}{27}=\frac{60}{27}=\frac{20}{9}

So our answer is 2 \frac{2}{9}

      Hope this helps, have a great day! :D

6 0
2 years ago
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Alexus [3.1K]

Answer:

a)6

b)v^2-u^2/2a

Step-by-step explanation:

a)Given that,

u=12

a= -6

s=9

We know that,

v^2=u^2+2as

or, v^2=(12)^2+2×(-6)×9

or,v^2=144-108

or,v^2=36

or, v=√36

∴v=6

         (Ans)

b)If ,v^2=u^2+2as

then, u^2+2as=v^2

or,2as=v^2-u^2

or, s=v^2-u^2/2a

∴s=v^2-u^2/2a

Hope ya find it helpful.. Thanks a lot...

6 0
3 years ago
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