2110014002
Level:
A
In one of the pictures given below is not a graph of a part of a geometric sequence. Choose this graph.
Geometric sequences
2110014001
Level:
A
In one of the pictures given below is not a graph of a part of a geometric sequence. Choose this graph.
2010005509
Level:
C
How many numbers do we need to insert between the numbers \( 5 \) and \( 640 \) so that the inserted numbers with the given two numbers are consecutive terms of a geometric sequence? The sum of all numbers inserted must be \( 630 \).
\( 6 \)
\( 4 \)
\( 3 \)
\( 5 \)
\( 7 \)
2010005508
Level:
C
The half-life of Copper-60 is approximately \( 24 \) minutes. How long will it take before its weight decreases from \( 1\,024\,\mathrm{g} \) to \( 8\,\mathrm{g} \)?
\( 2 \) hours \( 48 \) minutes
\( 3 \) hours \( 9 \) minutes
\( 3 \) hours \( 30 \) minutes
\( 2 \) hours \( 27 \) minutes
\( 3 \) hours \( 51 \) minutes
2010005507
Level:
C
A motorbike depreciates (loses value) at the rate of \(12\, \%\)
per year. After how many full years will the value of the motorbike decrease to less than one third of its initial value?
\(9\)
\(6\)
\(7\)
\(8\)
\(10\)
2010005506
Level:
B
The sum of the first \( n \) terms of a geometric sequence is \( 1 \), the common ratio is \( -3 \) and the first term equals \( \frac17 \). Find \( n \).
\( 3\)
\( 4 \)
\( 5 \)
\( 6 \)
\( 2 \)
2010005505
Level:
B
The sum of the first two terms of a geometric sequence is \( 54 \) and its first term equals \( 3 \). Which of the following statements about its common ratio \( q \) is not valid?
\( q \) is an even number.
\( q > 10 \)
\( q < 54 \)
\( q \) is a prime number.
\( q \) is a divisor of \( 51 \).
2010005504
Level:
B
Find the sum of the first five terms of the geometric sequence \( \{a_n\}_{n=1}^{\infty} \), if: \[ \begin{aligned} a_1+a_3&=-10, \\ a_1+a_2&=0. \end{aligned} \]
\( -5 \)
\( 5 \)
\( 0 \)
\( -1 \)
\( 1\)
2010005503
Level:
B
Find the first term of the geometric sequence \( \{a_n\}_{n=1}^{\infty} \), if: \[\begin{aligned} a_5\cdot a_6&=-9, \\ a_6-a_5&=6. \end{aligned} \]
\( -3 \)
\( 3 \)
\( -1 \)
\( 1 \)
\( -9 \)
2010005502
Level:
B
The sum of the first three terms of a geometric sequence is \( \frac{13}9 \) and the common ratio is \( \frac13 \). Find the sum of all the terms from the \( 3 \)rd to the \( 5 \)th of the sequence.
\( \frac{13}{81} \)
\( \frac{10}{81} \)
\( \frac1{27} \)
\( \frac{40}{81} \)
\( \frac{121}{81} \)