Geometric sequences

2010004905

Level:

The \( n \)th term of a geometric sequence is \( 4^{n-1}\cdot5^{2-n} \). Find the second term and the common ratio.

\( a_2=4 \), \( q=\frac45 \)

\( a_2=4 \), \( q=\frac54 \)

\( a_2=5 \), \( q=\frac45 \)

\( a_2=4 \), \( q=20 \)

\( a_2=5 \), \( q=20 \)

2010004906

Level:

The picture shows a part of the graph of the geometric sequence. What is the explicit formula for the \(n\)th term of the following geometric sequence?

\( a_n =2\cdot5^{n-1}\)

\( a_n =2\cdot5^{n}\)

\( a_n =5^{n-1}\)

\( a_n =2\cdot5^{n+1}\)

2010004907

Level:

The picture shows a part of the graph of the geometric sequence. What is the explicit formula for the \(n\)th term of the following geometric sequence?

\( a_n =4\cdot3^{n+1}\)

\( a_n =4\cdot3^{n}\)

\( a_n =4\cdot3^{n-1}\)

\( a_n =3^{n-1}\)

2010014003

Level:

First five terms of four sequences are given. One of these sequences is not a geometric sequence. Choose this sequence.

\( \frac12 , \frac14, \frac16, \frac18, \frac1{10}\)

\(1,-1,1,-1,1\)

\(2,2,2,2,2\)

\( 6,12,24,48,96\)

2010014004

Level:

First five terms of four sequences are given. One of these sequences is not a geometric sequence. Choose this sequence.

\( \frac13 , \frac16, \frac19, \frac1{12}, \frac1{15}\)

\(2,-2,2,-2,2\)

\(7,7,7,7,7\)

\( 1,4,4^2,4^3,4^4\)

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?