2010004904
Level:
A
The \(n\)th term of a geometric sequence is \(\frac29 \), the common ratio is \( \frac13 \) and the fourth term is \( 6 \). Find \( n \).
\( 7 \)
\( 8 \)
\( 6 \)
\( 10 \)
\( 5 \)
Geometric sequences
2010004903
Level:
A
The seventh term of a geometric sequence is \( 32 \) and the tenth term is \( 4 \). Choose the correct formula to find the eighth term of this sequence.
\( a_8=32\cdot\sqrt[3]{\frac4{32}} \)
\( a_8=32\cdot\sqrt[3]{\frac{32}4} \)
\( a_8=4\cdot\sqrt[3]{\frac4{32}} \)
\( a_8=4\cdot\sqrt[3]{\frac{32}4} \)
\( a_8=8\cdot\sqrt[3]{\frac3{24}} \)
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
\(x\).
\[
25\, ,\ 5\, ,\ x\, ,\ a
\]
\(1\)
\(\frac{1}
{5}\)
\(-\frac{1}
{5}\)
\(- 1\)
Fifth Term of Geometric Sequence
Submitted by ladislav.foltyn on Thu, 05/23/2019 - 10:00Question:
Find the $5$th term of the given geometric sequence, where $a_n$ denotes the $n$th term, $q$ is common ratio, and $s_n$ is the sum of the first $n$ terms of the sequence.
1003134604
Level:
B
Find the $5$th term of a geometric sequence $\{a_n\}_{n=1}^{\infty}$, where $a_1\cdot a_3\cdot a_5=x^3$, and $\frac{a_4}{a_2} =y^4$.
$xy^4$
$\frac x{y^4}$
$\frac x{y^2}$
$x$
$xy^2$
1003134603
Level:
B
The sum of the first five terms of a geometric sequence is less than $1$ and the common ratio is $10$. Determine all possible values of the first term.
$ a_1 < \frac1{11111}$, $a_1\in\mathbb{R}$
$ -\frac1{10^5} < a_1 < \frac1{10^5}$, $a_1\in\mathbb{R}$
$a_1 < \frac1{99999}$, $a_1\in\mathbb{R}$
$a_1 < 10^{-4}$, $a_1\in\mathbb{R}$
$a_1 < 10^{-5}$, $a_1\in\mathbb{R}$
1003134602
Level:
B
The sum of the second and the third term of a geometric sequence is $6\log3$ and the common ratio is $2$. Find the sum of the first three terms.
$7\log3$
$2\log3^6$
$2\log6$
$\log9$
$3\log6$
1003134601
Level:
A
The fifth term of a geometric sequence is $4\sqrt2$ and the second term is $2$. Find the fourth term.
$4$
$2\sqrt2$
$3\sqrt2$
$\sqrt2$
$2$
1003158507
Level:
C
Let there be a row of five yellow cubes lying side by side. The first cube has an edge length of \( 100\,\mathrm{cm} \) and each next cube has an edge length by \( 10\,\mathrm{cm} \) shorter than the previous one. Let there be a second row of five blue cubes lying side by side. The first blue cube has an edge length of \( 100\,\mathrm{cm} \) and each next cube has an edge length by \( 10\% \) smaller than the previous one. What is the difference between the length of these two rows?
\( 9.51\,\mathrm{cm} \)
\( 34.51\,\mathrm{cm} \)
\( 0\,\mathrm{cm} \)
\( 20\,\mathrm{cm} \)
\( 20.51\,\mathrm{cm} \)