9000072706
Level:
B
We are given five consecutive terms of an arithmetic sequence. Find
\(x\).
\[
5\, ,\ a\, ,\ b\, ,\ x\, ,\ 6
\]
\(x = 5.75\)
\(x = 5.5\)
\(x = 5.8\)
\(x = 5\frac{2}
{3}\)
B
9000072705
Level:
B
We are given four consecutive terms of an arithmetic sequence. Find
\(x\).
\[
3\, ,\ a\, ,\ 0\, ,\ x
\]
\(x = -1.5\)
\(x = -3\)
\(x = 6\)
\(x = -6\)
9000073002
Level:
B
Consider a geometric sequence \((a_{n})_{n=1}^{\infty }\).
Let \(q\) be the quotient
and \(s_{n}\) be the sum
of the first \(n\)
terms. Given \(a_{6} = 5\)
and \(q = 1\),
find the sum of the first five terms of the sequence.
\(s_{5} = 25\)
\(s_{5} = 31\)
\(s_{5} = 6\)
\(s_{5} = 30\)
9000072708
Level:
B
We are given six consecutive terms of an arithmetic sequence. Find
\(x\).
\[
\frac52,\ a,\ x,\ b,\ c,\ 5
\]
\(x = 3.5\)
\(x = 3\)
\(x = 4\)
\(x = 3.75\)
9000072806
Level:
B
The following numbers form a geometric sequence. Find
\(x\).
\[
2\, ,\ 1\, ,\ a\, ,\ x
\]
\(\frac{1}
{4}\)
\(\frac{1}
{2}\)
\(-\frac{1}
{2}\)
\(- 1\)
9000073408
Level:
B
Find the values of \(x\)
which ensure that the following infinite series is convergent.
\[
\sum _{n=1}^{\infty }\log ^{n-1}x
\]
\(x\in \left ( \frac{1}
{10};10\right )\)
\(x\in (1;+\infty )\)
\(x\in (1;10)\)
\(x\in \mathbb{R}^{+}\)
9000073407
Level:
B
Find all the values of \(x\)
such that the following infinite series is convergent.
\[
1 + 3 - 2x + (3 - 2x)^{2} + (3 - 2x)^{3}+\cdots
\]
\(x\in (1;2)\)
\(x\in (-\infty ;-1)\)
\(x\in (1;+\infty )\)
\(x\in \mathbb{R}\)
9000072701
Level:
B
The following numbers form an arithmetic sequence. Find
\(x\).
\[
1\, ,\ x\, ,\ 3
\]
\(x = 2\)
\(x = -2\)
\(x = 2.5\)
\(x = 1.5\)
9000072808
Level:
B
The following numbers form a geometric sequence. Find
\(x\).
\[
-2\, ,\ 4\, ,\ x
\]
\(- 8\)
\(8\)
\(6\)
\(16\)
9000072807
Level:
B
The following numbers form a geometric sequence. The third term satisfies
\(a < 0\). Find
\(x\).
\[
x\, ,\ 1\, ,\ a\, ,\ \frac{1}
{9}
\]
\(- 3\)
\(9\)
\(3\)
\(-\frac{1}
{3}\)