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Minchanka [31]
3 years ago
5

What is the sum of the first five terms of a geometric series with a1 = 6 and r = 1/3?

Mathematics
2 answers:
kakasveta [241]3 years ago
8 0

Answer:

242/27

Step-by-step explanation:

tresset_1 [31]3 years ago
6 0
The sum of the terms of a geometric sequence with common ratio lesser than 1 is calculated through the equation,

                                  Sn = (a1) x (1 - r^n) / (1 - r)
Substituting the known values,
                                 S5 = (6) x (1 - (1/3)^5) / (1 - 1/3) = 242/27
Thus, the sum of the first five terms is approximately equal to 8.96. 

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Write an explicit equation for the following sequence.<br><br> 100, 97, 94, 91, ...
pishuonlain [190]

Answer:

a_{n} = 103 - 3n

Step-by-step explanation:

there is a common difference between consecutive terms , that is

97 - 100 = 94 - 97 = 91 - 94 = - 3

This indicates the sequence is arithmetic with explicit equation

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 100 and d = - 3 , then

a_{n} = 100 - 3(n - 1) = 100 - 3n + 3 = 103 - 3n

6 0
2 years ago
If 4x^2 - 100 = 0 then the roots of the equation are
iVinArrow [24]
4x² - 100 = 0
<u>     + 100  + 100</u>
         <u> 4x²</u> = <u>100</u>
          4        4
           x² = 25
            x = <u>+</u>5
 4(5)² - 100 = 0
4(25) - 100 = 0
  100 - 100 = 0
               0 = 0

4(-5)² - 100 = 0
 4(25) - 100 = 0
   100 - 100 = 0
                0 = 0

The roots of the equation is positive or negative 5.
8 0
2 years ago
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In a family there was give sons. The oldest son is 11 3/4 years old, and every next younger brother is younger than the next by
aleksklad [387]

Answer:

5.5

Step-by-step explanation:

5 0
2 years ago
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The sum of the measures of two angles is 107.3º. One angle has a measure of 51º. What is the measure of the second angle?
babunello [35]

Answer:

56.3°

Step-by-step explanation:

If the total is 107.3° just subtract 51° to get 56.3°

3 0
3 years ago
Just need to know what x is haha
marishachu [46]

Answer: x=14

Step-by-step explanation:

The angles in a triangle are equal to 180 so

6x + 3 + 5x + x + 9 = 180

12x + 12 = 180

      -12     -12

12x = 168

x = 14

4 0
3 years ago
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