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 \(a_{13}\).
\(31\)
\(22\)
\(25\)
\(28\)
\(34\)
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.
\(7\)
\(9\)
\(11\)
\(13\)
\(15\)
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.
\(501\, \mathrm{cm}^{2}\)
\(315\, \mathrm{cm}^{2}\)
\(615\, \mathrm{cm}^{2}\)
\(805\, \mathrm{cm}^{2}\)
\(1\: 215\, \mathrm{cm}^{2}\)