Geometric sequences

9000073004

Level:

Consider a geometric sequence

(a_{n})_{n = 1}^{\infty}

. Let

q

be the quotient and

s_{n}

be the sum of the first

n

terms. Given

a_{1} = 1

a_{3} = 4

and

a_{2} < 0

, find the sum of the first four terms of the sequence.

s_{4} = - 5

s_{4} = 15

s_{4} = 14

s_{4} = 8

9000073005

Level:

Consider a geometric sequence

(a_{n})_{n = 1}^{\infty}

. Let

q

be the quotient and

s_{n}

be the sum of the first

n

terms. Given

a_{2} = 1

and

a_{3} = 10

, find the sum of the first four terms of the sequence.

s_{4} = 111.1

s_{4} = 99.9

s_{4} = 111

s_{4} = 100

9000073006

Level:

Consider a geometric sequence

(a_{n})_{n = 1}^{\infty}

. Let

q

be the quotient and

s_{n}

be the sum of the first

n

terms. Given

a_{1} = 1

and

a_{4} = - 8

, find the sum of the first five terms of the sequence.

s_{5} = 11

s_{5} = 31

s_{5} = 16

s_{5} = - 16

9000073007

Level:

Consider a geometric sequence

(a_{n})_{n = 1}^{\infty}

. Let

q

be the quotient and

s_{n}

be the sum of the first

n

terms. Given

a_{1} = - 1 000

and

a_{2} = 100

, find the sum of the first four terms of the sequence.

s_{4} = - 909

s_{4} = - 900

s_{4} = 911

s_{4} = - 911

Karel made a resolution to go running. On the first day he ran one kilometre. Every day he extended the distance run by a quarter of the distance run on the previous day. How many whole kilometres did he run on the tenth day?

7

9

8

6

11

1003109202

Level:

A blouse is on sale and its price was reduced twice, each time by ten percent. The difference between its original and its final price is

133 CZK

. What was the blouse original price before the discounts?

700 CZK

665 CZK

1 330 CZK

1 400 CZK

750 CZK

1003109203

Level:

The half-life of Francium is

21

minutes. How long will it take before its weight decreases from

512 g

1 g

3

hours

9

minutes

2

hours

48

minutes

3

hours

30

minutes

2

hours

27

minutes

3

hours

51

minutes

1003109204

Level:

Candles are being lit at a commemoration in the square. Gradually, every

15

seconds, two candles are lit from one already burning candle. It also took

15

seconds to lit the first candle. After

4

minutes, all candles were lit. How many candles were finally burning in the square?

65 535

32 767

32 768

131 070

131 071

1003109206

Level:

2016

, the population of the Czech Republic increased by

25 000

10 578 820

inhabitants. How many inhabitants will there live in the Czech Republic at the end of the year

2026

, if the percentage increase is the same every year?

10 832 100

10 828 820

10 846 286

10 831 495

10 603 879

1003109207

Level:

2015

8 688

choir members sang in the largest gospel choir in Manila. Imagine, the conductor wrote an e-mail on January

1

st to three choir members. Each of them forwarded the e-mail to other three choir members on the next day and so on... On which day would all members receive the e-mail?

8

January

15

January

2

February

8

February

12

January

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