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 \(363\).
\(n = 5\)
\(n = 2\)
\(n = 3\)
\(n = 4\)
\(n = 6\)
Geometric Sequences
9000070504
Level:
C
The geometric sequence is formed by consecutive powers of the number
\(3\). The eighth
term is \(a_{8} = 3^{10}\).
Find the sum of the first five terms.
\(3\: 267\)
\(1\: 089\)
\(2\: 178\)
\(4\: 356\)
\(6\: 543\)
9000070507
Level:
C
A car depreciates (loses value) at the rate of \(15\, \%\)
per year. After how many full years will the value of the car decrease to less than one quarter of its initial value?
\(9\)
\(6\)
\(7\)
\(8\)
\(10\)
9000070501
Level:
B
Consider the geometric sequence with \(a_{2} = 50\)
and \(a_{3} = 25\).
Find the sum of the first four terms.
\(187.5\)
\(93.75\)
\(250\)
\(375\)
\(500\)
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.
\(57\, \mathrm{cm}^{2}\)
\(28.5\, \mathrm{cm}^{2}\)
\(27\, \mathrm{cm}^{2}\)
\(35\, \mathrm{cm}^{2}\)
\(45\, \mathrm{cm}^{2}\)
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.
\(x = 2\)
\(x = 4\)
\(x = 10^{2}\)
\(x = \frac{1}
{2}\)
\(x = \frac{1}
{100}\)
9000068701
Level:
B
Identify the real number \(x\)
which converts the numbers \(a_{1} = 10^{2}\),
\(a_{2} = 10^{3}\) and
\(a_{3} = x\) into
three consecutive numbers of a geometric series.
\(x = 10\: 000\)
\(x = 1\: 000\)
\(x = 1\: 900\)
\(x = 1\: 990\)
\(x = 100\: 000\)