9000068706
Level:
B
Identify the real number \(x\)
which converts the numbers \(a_{1} = x + 14\),
\(a_{2} = x + 2\) and
\(a_{3} = x - 4\) into
three consecutive numbers of a geometric series.
\(x = 10\)
\(x = 5\)
\(x = 2.5\)
\(x = 2\)
\(x = -5\)
Geometric sequences
9000068707
Level:
B
Identify the real number \(x\)
which converts the numbers \(a_{1} = x^{2} - 110\),
\(a_{2} = x^{2}\) and
\(a_{3} = x^{2} - 1\: 100\) into
three consecutive numbers of a geometric series.
\(x = -10\)
\(x = -1\)
\(x = -2\)
\(x = -4\)
\(x = -110\)
9000068708
Level:
B
Identify the real number \(x\)
which converts the numbers \(a_{1} = 2^{x-4}\),
\(a_{2} = 1\) and
\(a_{3} = 2^{x}\) into
three consecutive terms of a geometric series.
\(x = 2\)
\(x = 1\)
\(x =\log 2\)
\(x = 10\)
\(x = 100\)
9000068709
Level:
B
Identify the real number \(x\)
which converts the numbers \(a_{1} =\log x\),
\(a_{2} = 2 +\log x\) and
\(a_{3} = 4\log x\) into
three consecutive numbers of a geometric series.
\(x = 100\)
\(x = 1\)
\(x =\log 2\)
\(x = 2\)
\(x = 10\)
9000068710
Level:
B
Identify the real number \(x\)
which converts the numbers \(a_{1} = 10^{2x+2}\),
\(a_{2} = 10^{4x+1}\) and
\(a_{3} = 10^{12}\) into
three consecutive numbers of a geometric series.
\(x = 2\)
\(x = 4\)
\(x = 10^{2}\)
\(x = \frac{1}
{2}\)
\(x = \frac{1}
{100}\)
9000070501
Level:
B
Consider the geometric sequence with \(a_{2} = 50\)
and \(a_{3} = 25\).
Find the sum of the first four terms.
\(187.5\)
\(93.75\)
\(250\)
\(375\)
\(500\)
9000070502
Level:
B
Consider the geometric sequence with the first term
\(a_{1} = 243\) and quotient
\(q = \frac{1}
{3}\). Find
\(n\) such that the
sum of the first \(n\)
terms equals \(363\).
\(n = 5\)
\(n = 2\)
\(n = 3\)
\(n = 4\)
\(n = 6\)
9000072801
Level:
B
The following numbers form a geometric sequence. Find
\(x\).
\[
2\, ,\ 4\, ,\ x
\]
\(8\)
\(5\)
\(6\)
\(16\)
9000072802
Level:
B
The following numbers form a geometric sequence. Find
\(x\).
\[
100\, ,\ a\, ,\ 1\, ,\ b\, ,\ x
\]
\(0.01\)
\(- 100\)
\(0.1\)
\(- 10\)
9000072803
Level:
B
The following numbers form a geometric sequence. The last term satisfies
\(a > 0\). Find
\(x\).
\[
1\, ,\ x\, ,\ 2\, ,\ a
\]
\(\sqrt{2}\)
\(-\sqrt{2}\)
\(1.5\)
\(- 1.5\)