2010004911
Level:
B
At which term does the geometric sequence \( (4096\, ,\ 1024 \, ,\ 256 \, , \ 64\, , \ \dots)\) begin to have values less than \(1\)?
\(8\)
\(7\)
\(6\)
\(9\)
B
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?
\( 8\)
\(9\)
\(7\)
\(10\)
2010004902
Level:
B
The following numbers form a geometric sequence. The fourth term satisfies
\(a < 0\). Find
\(x\).
\[
7\, ,\ x\, ,\ \frac{1}
{7}\, ,\ a
\]
\(- 1\)
\(1\)
\(-7\)
\(-\frac{1}
{7}\)
2010004901
Level:
B
The following numbers form a geometric sequence. Find
\(x\).
\[
25\, ,\ 5\, ,\ x\, ,\ a
\]
\(1\)
\(\frac{1}
{5}\)
\(-\frac{1}
{5}\)
\(- 1\)
2010004808
Level:
B
Assuming \(x\not \in \{-4;-1;0;4\}\),
simplify the following expression.
\[
\left(\frac{x+1}
{x^{2} +4x}\right)^{-1}\cdot \frac{x^{2} +x}
{x^2 - 16}
\]
\(\frac{x^2}
{x-4} \)
\(\frac{x^2}
{x+4} \)
\(\frac{2x}
{x-4} \)
\(\frac{x}
{x-4} \)
2010004807
Level:
B
Write the number \(\root{12}\of{5^{-4}}\)
as a power with a rational exponent.
\(5^{-\frac{1}
{3} }\)
\(5^{\frac{1}
{3} }\)
\(5^{3}\)
\(5^{-3}\)
2010004806
Level:
B
Simplify the expression \(0.3^{\frac{4}
{5} }\cdot 0.3^{-\frac{3}
{10} }\)
and write the result using a root.
\(\sqrt{0.3}\)
\(\root{5}\of{0.3}\)
\(\root{10}\of{0.3^{7}}\)
\(\root{3}\of{0.3^8}\)
2010004804
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x}\cdot \root{5}\of{x^{3}}
\]
\(\root{15}\of{x^{14}}\)
\(\root{5}\of{x}\)
\(\root{15}\of{x^{4}}\)
\(\sqrt{x}\)