9000064808
Level:
C
The sum of the first eight terms of an arithmetic sequence is
\(44\).
The sum of the next four terms is bigger than this value by
\(50\). Find the
thirteenth term \(a_{13}\).
\(31\)
\(22\)
\(25\)
\(28\)
\(34\)
Arithmetic sequences
9000064806
Level:
B
The arithmetic sequence is defined by the first term
\(a_{1} = 17\) and the
fifth term \(a_{5} = 11\).
Find the term which is seven times smaller than the third term of the sequence.
\(a_{11}\)
\(a_{2}\)
\(a_{8}\)
\(a_{17}\)
\(a_{21}\)
9000064801
Level:
C
The sides of a right triangle form three consecutive terms of an arithmetic sequence. The perimeter
of the triangle is \(60\, \mathrm{cm}\).
Find the hypotenuse of the triangle (the longest side).
\(25\, \mathrm{cm}\)
\(12\, \mathrm{cm}\)
\(15\, \mathrm{cm}\)
\(20\, \mathrm{cm}\)
\(30\, \mathrm{cm}\)
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.
\(7\)
\(9\)
\(11\)
\(13\)
\(15\)
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.
\(x = -0.4\)
\(x = 0.4\)
\(x = 2.5\)
\(x = -2.5\)
\(x = 5\)