2010004914
Level:
B
Identify the real number \(x\)
which converts the numbers \(a_{1} = 3^{x-6}\),
\(a_{2} = 1\) and
\(a_{3} = 3^{x}\) into
three consecutive terms of a geometric series.
\(x = 3\)
\(x = 1\)
\(x =\log 3\)
\(x = 10\)
\(x = 100\)
Geometric sequences
2010004913
Level:
B
At which term does the geometric sequence \( (8\, ;\ 10 \, ;\ 12.5 \, ; \ 15.625 \, ; \ \dots)\) exceed \(80\)? (Use a calculator.)
\(12\)
\(11\)
\(13\)
\(14\)
2010004912
Level:
B
At which term does the geometric sequence \( (10\, ;\ 12 \, ;\ 14.4 \, ; \ 17.28 \, ; \ \dots)\) exceed \(100\)? (Use a calculator.)
\(14\)
\(13\)
\(12\)
\(15\)
2010004911
Level:
B
At which term does the geometric sequence \( (4096\, ,\ 1024 \, ,\ 256 \, , \ 64\, , \ \dots)\) begin to have values less than \(1\)?
\(8\)
\(7\)
\(6\)
\(9\)
2010004910
Level:
B
At which term does the geometric sequence \( (2187\, ,\ 729 \, ,\ 243 \, , \ 81\, , \ \dots)\) begin to have values less than \(1\)?
\(9\)
\(8\)
\(7\)
\(10\)
2010004909
Level:
B
At which term does the geometric sequence \( \left( \frac{1}{4096}\, ,\ \frac{1}{1024}\, ,\ \frac{1}{256}\, ,\ \frac{1}{64}\, ,\ \dots \right)\) begin to have natural values?
\( 7\)
\(8\)
\(6\)
\(9\)
2010004908
Level:
B
At which term does the geometric sequence \( \left( \frac{1}{2187}\, ,\ \frac{1}{729}\, ,\ \frac{1}{243}\, ,\ \frac{1}{81}\, ,\ \dots \right)\) begin to have natural values?
\( 8\)
\(9\)
\(7\)
\(10\)
2010004907
Level:
A
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?
\( a_n =4\cdot3^{n+1}\)
\( a_n =4\cdot3^{n}\)
\( a_n =4\cdot3^{n-1}\)
\( a_n =3^{n-1}\)
2010004906
Level:
A
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?
\( a_n =2\cdot5^{n-1}\)
\( a_n =2\cdot5^{n}\)
\( a_n =5^{n-1}\)
\( a_n =2\cdot5^{n+1}\)
2010004905
Level:
A
The \( n \)th term of a geometric sequence is \( 4^{n-1}\cdot5^{2-n} \). Find the second term and the common ratio.
\( a_2=4 \), \( q=\frac45 \)
\( a_2=4 \), \( q=\frac54 \)
\( a_2=5 \), \( q=\frac45 \)
\( a_2=4 \), \( q=20 \)
\( a_2=5 \), \( q=20 \)