$Math-Quiz$

Test: Geometric Series I - Ambitious

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Question 1: Express the term of a geometric progression

a_{18}

through its another term

a_{12}

and its common ratio

r

a_{18} = a_{12} + 6 r

a_{18} = a_{12} \times r^{6}

a_{18} = \frac{a_{12}}{r^{6}}

a_{18} = a_{12} \times 6 r

Question 2: (

a_{n}

) is a geometric sequence. Put the sign between these two expressions:

a_{4} \times a_{21} ? a_{8} \times a_{17}

a_{4} \times a_{21} = a_{8} \times a_{17}

a_{4} \times a_{21} \geq a_{8} \times a_{17}

a_{4} \times a_{21} < a_{8} \times a_{17}

a_{4} \times a_{21} > a_{8} \times a_{17}

Question 3: Find the initial term of the geometric sequence (

a_{n}

), if

r = \frac{1}{2}

a_{4} = \frac{1}{32}

\frac{1}{2}

\frac{1}{4}

\frac{1}{8}

4

Question 4:

192

is a term of a geometric sequence:

\frac{2}{3}, 3, 6, \dots

. Find its number.

10

5

6

7

Question 5: What two numbers should be put between

3

and

192

two create a geometric progression?

66; 129

52; 103

12; 48

- 12; 48

Question 6: Find the sum of the first four terms of the geometric sequence (

a_{n}

) if

a_{4} = 189, r = - 3

70

140

\frac{560}{3}

3780

Question 7: Find the sum of the first six terms of the geometric sequence (

a_{n}

), if

a_{1} = 5, a_{5} = 125, r > 0

155 (\sqrt{5} + 1)

\frac{\sqrt{5} - 1}{620}

155 (\sqrt{5} + 5)

155

Question 8: Geometric sequence is given by a formula

a_{n} = 10 \times 3^{n}

. Find the sum of the first five terms.

2400

2430

1200

900

Question 9: The common ratio of the geometric progression (

a_{n}

) is

r = 2

. Find the initial term if the sum of the first four terms equals

60

4

1

8

2

Question 10: Find the sum of the infinite geometric progression (

a_{n}

), if

a_{2} = 18, r = \frac{1}{3}

72

81

162

27

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