9000064803
Level:
C
Suppose three numbers form three consecutive terms of an arithmetic sequence. The sum of these
numbers is \(33\) and
the product is \(1\: 155\).
Find the smallest of these three numbers.
\(7\)
\(9\)
\(11\)
\(13\)
\(15\)
Arithmetic Sequences
9000064804
Level:
C
An arithmetic sequence is formed by consecutive odd integers. The twelfth term is
\( 53\). Find
the sum of the first five terms.
\(175\)
\(151\)
\(163\)
\(187\)
\(199\)
9000064807
Level:
C
Find the sum of the integers which satisfy the following inequality.
\[
x^{2} - 8x - 153\leq 0
\]
\(108\)
\(162\)
\(91\)
\(78\)
\(56\)
9000064805
Level:
C
The sides of a box form three consecutive terms of an arithmetic sequence. The volume of the box is
\(665\, \mathrm{cm}^{3}\). The shortest
side is \(5\, \mathrm{cm}\).
Find the surface area of the box.
\(501\, \mathrm{cm}^{2}\)
\(315\, \mathrm{cm}^{2}\)
\(615\, \mathrm{cm}^{2}\)
\(805\, \mathrm{cm}^{2}\)
\(1\: 215\, \mathrm{cm}^{2}\)
9000060601
Level:
B
Identify the real number \(x\) which
ensures that the numbers \(a_{1} = 10^{2}\),
\(a_{2} = 10^{3}\) and
\(a_{3} = x\) are
three consecutive terms of an arithmetic sequence.
\(x = 1\: 900\)
\(x = 1\: 000\)
\(x = 10\: 000\)
\(x = 1\: 990\)
\(x = 100\: 000\)
9000060605
Level:
B
Identify the real number \(x\) which
ensures that the numbers \(a_{1} = x^{2} + 10\),
\(a_{2} = x^{2} + 2x\) and
\(a_{3} = x^{2}\) are
three consecutive terms of an arithmetic sequence.
\(x = 2.5\)
\(x = 0\)
\(x = 2\)
\(x = 5\)
\(x = -5\)
9000060607
Level:
B
Identify the real number \(x\) which
ensures that the numbers \(a_{1} = x^{2} + 2x\),
\(a_{2} = 2x^{2} + 4x\) and
\(a_{3} = x^{2} - 2x - 8\) are
three consecutive terms of an arithmetic sequence.
\(x = -2\)
\(x = 0\)
\(x = 2\)
\(x = 4\)
\(x = -4\)
9000060609
Level:
B
Identify the real number \(x\) which
ensures that the numbers \(a_{1} =\log (x + 2)\),
\(a_{2} =\log (3x + 6)\) and
\(a_{3} =\log 18\) are
three consecutive terms of an arithmetic sequence.
\(x = 0\)
\(x =\log 3\)
\(x = 3\)
\(x = 8\)
\(x = 18\)
9000060603
Level:
B
Identify the real number \(x\) which
ensures that the numbers \(a_{1} = -x\),
\(a_{2} = -5\) and
\(a_{3} = 0\) are
three consecutive terms of an arithmetic sequence.
\(x = 10\)
\(x = 0\)
\(x = -5\)
\(x = 5\)
\(x = -10\)
9000060606
Level:
B
Identify the real number \(x\) which
ensures that the numbers \(a_{1} = 5x + 1\),
\(a_{2} = x\) and
\(a_{3} = 7x + 3\) are
three consecutive terms of an arithmetic sequence.
\(x = -0.4\)
\(x = 0.4\)
\(x = 2.5\)
\(x = -2.5\)
\(x = 5\)