Geometric sequences

9000070503

Level:

Three numbers form a geometric sequence. The sum of these numbers is

39

and the product is

1 000

. Find the smallest of these numbers.

4

2

2.5

10

25

9000070505

Level:

The dimensions of the box form a geometric sequence. The volume of the box is

27 {cm}^{3}

and the length of the shortest side is

2 cm

. Find the surface area of the box.

57 {cm}^{2}

28.5 {cm}^{2}

27 {cm}^{2}

35 {cm}^{2}

45 {cm}^{2}

9000070506

Level:

The intensity of the light is reduced by

8 %

when the light shines through the glass panel. How much of the light intensity remains if the light shines through

6

glass panels?

60.6 %

39.4 %

52 %

48 %

3.14 %

9000068702

Level:

Identify the real number

x

which converts the numbers

a_{1} = - 12

a_{2} = x

and

a_{3} = - 48

into three consecutive numbers of a geometric series.

x = - 24

x = 0

x = 6

x = 12

x = - 2

9000068703

Level:

Identify the real number

x

which converts the numbers

a_{1} = - x

a_{2} = - 5

and

a_{3} = 5

into three consecutive numbers of a geometric series.

x = - 5

x = 0

x = 5

x = - 10

x = 10

9000068708

Level:

Identify the real number

x

which converts the numbers

a_{1} = 2^{x - 4}

a_{2} = 1

and

a_{3} = 2^{x}

into three consecutive terms of a geometric series.

x = 2

x = 1

x = \log 2

x = 10

x = 100

9000068705

Level:

Identify the real number

x

which converts the numbers

a_{1} = x - 6

a_{2} = x

and

a_{3} = - x

into three consecutive numbers of a geometric series.

x = 3

x = 0

x = 2

x = 2.5

x = - 12

9000068706

Level:

Identify the real number

x

which converts the numbers

a_{1} = x + 14

a_{2} = x + 2

and

a_{3} = x - 4

into three consecutive numbers of a geometric series.

x = 10

x = 5

x = 2.5

x = 2

x = - 5

9000068704

Level:

Identify the real number

x

which converts the numbers

a_{1} = x

a_{2} = x + 5

and

a_{3} = 4 x

into three consecutive numbers of a geometric series.

x = 5

x = 1

x = 2

x = 3

x = 4

9000068707

Level:

Identify the real number

x

which converts the numbers

a_{1} = x^{2} - 110

a_{2} = x^{2}

and

a_{3} = x^{2} - 1 100

into three consecutive numbers of a geometric series.

x = - 10

x = - 1

x = - 2

x = - 4

x = - 110

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