9000072807
Level:
B
The following numbers form a geometric sequence. The third term satisfies
\(a < 0\). Find
\(x\).
\[
x\, ,\ 1\, ,\ a\, ,\ \frac{1}
{9}
\]
\(- 3\)
\(9\)
\(3\)
\(-\frac{1}
{3}\)
Geometric sequences
9000072808
Level:
B
The following numbers form a geometric sequence. Find
\(x\).
\[
-2\, ,\ 4\, ,\ x
\]
\(- 8\)
\(8\)
\(6\)
\(16\)
9000073003
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 \(a_{1} = 1\),
\(a_{3} = 4\) and
\(a_{2} > 0\), find
the sum of the first four terms of the sequence.
\(s_{4} = 15\)
\(s_{4} = -5\)
\(s_{4} = 14\)
\(s_{4} = 8\)
9000072802
Level:
B
The following numbers form a geometric sequence. Find
\(x\).
\[
100\, ,\ a\, ,\ 1\, ,\ b\, ,\ x
\]
\(0.01\)
\(- 100\)
\(0.1\)
\(- 10\)
9000072810
Level:
B
The following numbers form a geometric sequence. Find
\(x\).
\[
x\, ,\ 2\cdot 3\, ,\ 3\cdot 4
\]
\(1\cdot 3\)
\(1\cdot 1\)
\(1\cdot 2\)
\(1\cdot 4\)
9000073004
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 \(a_{1} = 1\),
\(a_{3} = 4\) and
\(a_{2} < 0\), find
the sum of the first four terms of the sequence.
\(s_{4} = -5\)
\(s_{4} = 15\)
\(s_{4} = 14\)
\(s_{4} = 8\)
9000073005
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 \(a_{2} = 1\)
and \(a_{3} = 10\),
find the sum of the first four terms of the sequence.
\(s_{4} = 111.1\)
\(s_{4} = 99.9\)
\(s_{4} = 111\)
\(s_{4} = 100\)
9000072809
Level:
B
The following numbers form a geometric sequence. Find
\(x\).
\[
1\, ,\ a\, ,\ x\, ,\ -1
\]
\(1\)
\(-\frac{1}
{3}\)
\(0\)
\(-\frac{2}
{3}\)
9000073007
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 \(a_{1} = -1\: 000\)
and \(a_{2} = 100\),
find the sum of the first four terms of the sequence.
\(s_{4} = -909\)
\(s_{4} = -900\)
\(s_{4} = 911\)
\(s_{4} = -911\)
9000073006
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 \(a_{1} = 1\)
and \(a_{4} = -8\),
find the sum of the first five terms of the sequence.
\(s_{5} = 11\)
\(s_{5} = 31\)
\(s_{5} = 16\)
\(s_{5} = -16\)