9000070501
Level:
B
Consider the geometric sequence with \(a_{2} = 50\)
and \(a_{3} = 25\).
Find the sum of the first four terms.
\(187.5\)
\(93.75\)
\(250\)
\(375\)
\(500\)
Geometric Sequences
9000070503
Level:
C
Three numbers form a geometric sequence. The sum of these numbers is
\(39\) and the
product is \(1\: 000\).
Find the smallest of these numbers.
\(4\)
\(2\)
\(2.5\)
\(10\)
\(25\)
9000070505
Level:
C
The dimensions of the box form a geometric sequence. The volume of the box is
\(27\, \mathrm{cm}^{3}\) and the length of
the shortest side is \(2\, \mathrm{cm}\).
Find the surface area of the box.
\(57\, \mathrm{cm}^{2}\)
\(28.5\, \mathrm{cm}^{2}\)
\(27\, \mathrm{cm}^{2}\)
\(35\, \mathrm{cm}^{2}\)
\(45\, \mathrm{cm}^{2}\)
9000070506
Level:
C
The intensity of the light is reduced by
\(8\, \%\) when the
light shines through the glass panel. How much of the light intensity remains if the light shines
through \(6\)
glass panels?
\(60.6\, \%\)
\(39.4\, \%\)
\(52\, \%\)
\(48\, \%\)
\(3.14\, \%\)
9000070508
Level:
C
The sum of the first three terms of a geometric sequence is
\(27\). The sum of the
next three terms is \(512\).
Find the quotient.
\(\frac{8}
{3}\)
\(2\)
\(3\)
\(\frac{3}
{2}\)
\(\frac{4}
{3}\)
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 \(363\).
\(n = 5\)
\(n = 2\)
\(n = 3\)
\(n = 4\)
\(n = 6\)
9000068704
Level:
B
Identify the real number \(x\)
which converts the numbers \(a_{1} = x\),
\(a_{2} = x + 5\) and
\(a_{3} = 4x\) into
three consecutive numbers of a geometric series.
\(x = 5\)
\(x = 1\)
\(x = 2\)
\(x = 3\)
\(x = 4\)
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.
\(x = -10\)
\(x = -1\)
\(x = -2\)
\(x = -4\)
\(x = -110\)
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.
\(x = 2\)
\(x = 4\)
\(x = 10^{2}\)
\(x = \frac{1}
{2}\)
\(x = \frac{1}
{100}\)