Geometric sequences
2010014004
Level:
A
First five terms of four sequences are given. One of these sequences is not a geometric sequence. Choose this sequence.
\( \frac13 , \frac16, \frac19, \frac1{12}, \frac1{15}\)
\(2,-2,2,-2,2\)
\(7,7,7,7,7\)
\( 1,4,4^2,4^3,4^4\)
2010014003
Level:
A
First five terms of four sequences are given. One of these sequences is not a geometric sequence. Choose this sequence.
\( \frac12 , \frac14, \frac16, \frac18, \frac1{10}\)
\(1,-1,1,-1,1\)
\(2,2,2,2,2\)
\( 6,12,24,48,96\)
2000014011
Level:
A
The picture shows a part of the graph of a geometric sequence. What is the common ratio of the geometric sequence?
\(-\frac12\)
\(-2\)
\(\frac12\)
\(\left(-\frac12\right)^n\)
2010014010
Level:
A
A sequence of patterns uses grey and purple squares. Identify the false statement about the numbers of squares in the patterns.
The numbers of grey squares in patterns do not form a geometric sequence.
The numbers of purple squares in patterns form a geometric sequence with an even common ratio.
The numbers of purple squares in patterns form a geometric sequence with a positive common ratio.
The numbers of grey squares in patterns form a geometric sequence with an even common ratio.
2010014009
Level:
A
A sequence of patterns uses grey and purple squares. Identify the false statement about the numbers of squares in the patterns.
The numbers of purple squares in patterns form a geometric sequence with an even common ratio.
The numbers of purple squares in patterns form a geometric sequence with a positive common ratio
The numbers of grey squares in patterns form a geometric sequence with a positive common ratio.
The numbers of grey squares in patterns form a geometric sequence with an even common ratio.
2010014008
Level:
A
The picture shows first three patterns formed by green dots. The numbers of dots in patterns correspond to terms of a geometric sequence. To which term corresponds a pattern that will use \(640\) dots?
Eighth
Seventh
Tenth
Nineth
2010014007
Level:
A
The picture shows first three patterns formed by green dots. The numbers of dots in patterns correspond to terms of a geometric sequence. To which term corresponds a pattern that will use \(192\) dots?
Seventh
Eighth
Tenth
Nineth
2110014006
Level:
C
Between the roots of the quadratic equation \(9x^2-35x+24=0\) insert two numbers, so that the numbers with the roots together form four consecutive terms of a geometric sequence. This part of the geometric sequence is shown in one of the graphs. Choose the graph.
2110014005
Level:
C
Between the roots of the quadratic equation \(4x^2-35x+54=0\) insert two numbers, so that the numbers with the roots together form four consecutive terms of a geometric sequence. This part of the geometric sequence is shown in one of the graphs. Choose the graph.
