9000065305
Level:
A
In the arithmetic sequence given by the relations
\(a_{1} =\pi \),
\(a_{n+1} = a_{n} + 2\pi \) find
\(a_{13}\).
\(a_{13} = 25\pi \)
\(a_{13} = 27\pi \)
\(a_{13} = 26\pi \)
\(a_{13} = 24\pi \)
Arithmetic sequences
9000065309
Level:
A
The arithmetic sequence satisfies \(a_{26} = 58\)
and \(a_{21} = 43\). Find the
first term \(a_{1}\) and
the common difference \(d\)
of this sequence.
\(a_{1} = -17;\ d = 3\)
\(a_{1} = -1;\ d = 5\)
\(a_{1} = 1;\ d = 15\)
\(a_{1} = -1;\ d = 3\)
9000065310
Level:
B
For the arithmetic sequence with \(a_{4} = 11\)
and \(a_{9} = -24\)
find the sum of the first fourteen terms.
\(- 189\)
\(189\)
\(198\)
\(- 198\)
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 \(a_{13}\).
\(31\)
\(22\)
\(25\)
\(28\)
\(34\)
9000060608
Level:
B
Identify the real number \(x\) which
ensures that the numbers \(a_{1} =\log x\),
\(a_{2} =\log(2x)\) and
\(a_{3} = 1\) are
three consecutive terms of an arithmetic sequence.
\(x = 2.5\)
\(x = 1\)
\(x =\log 2\)
\(x = 2\)
\(x = 1\)
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.
\(x = 10\)
\(x = 0\)
\(x = -5\)
\(x = 5\)
\(x = -10\)