9000072710
Level:
B
We are given seven consecutive terms of an arithmetic sequence. Find
\(x\).
\[
\frac{4}
{5}\, ,\ a\, ,\ b\, ,\ 0\, ,\ c\, ,\ d\, ,\ x
\]
\(x = -\frac{4}
{5}\)
\(x = \frac{5}
{4}\)
\(x = -\frac{5}
{4}\)
\(x = -\frac{8}
{5}\)
Arithmetic Sequences
9000072703
Level:
B
The following numbers form an arithmetic sequence. Find
\(x\).
\[
x\, ,\ 10\, ,\ 5
\]
\(x = 15\)
\(x = 20\)
\(x = 50\)
\(x = 5\)
9000072705
Level:
B
We are given four consecutive terms of an arithmetic sequence. Find
\(x\).
\[
3\, ,\ a\, ,\ 0\, ,\ x
\]
\(x = -1.5\)
\(x = -3\)
\(x = 6\)
\(x = -6\)
9000072708
Level:
B
We are given six consecutive terms of an arithmetic sequence. Find
\(x\).
\[
\frac52,\ a,\ x,\ b,\ c,\ 5
\]
\(x = 3.5\)
\(x = 3\)
\(x = 4\)
\(x = 3.75\)
9000072702
Level:
B
The following numbers form an arithmetic sequence. Find
\(x\).
\[
10\, ,\ 20\, ,\ x
\]
\(x = 30\)
\(x = 40\)
\(x = -20\)
\(x = -10\)
9000072704
Level:
B
We are given five consecutive terms of an arithmetic sequence. Find
\(x\).
\[
4\, ,\ a\, ,\ 8\, ,\ b\, ,\ x
\]
\(x = 12\)
\(x = 10\)
\(x = 14\)
\(x = 16\)
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.
\(a_{11}\)
\(a_{2}\)
\(a_{8}\)
\(a_{17}\)
\(a_{21}\)
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.
\(7\)
\(9\)
\(11\)
\(13\)
\(15\)
9000064807
Level:
C
Find the sum of the integers which satisfy the following inequality.
\[
x^{2} - 8x - 153\leq 0
\]
\(108\)
\(162\)
\(91\)
\(78\)
\(56\)
9000065301
Level:
A
Find the recurrence equations for the arithmetic sequence with the first term
\(a_{1} = 4\) and the common
difference \(d = -2\).
\(a_{1} = 4,\ a_{n+1} = a_{n} - 2,\ n\in\mathbb{N}\)
\(a_{1} = 4,\ a_{n+1} = a_{1} - 2,\ n\in\mathbb{N}\)
\(a_{n} = 4 + a_{n+2},\ n\in\mathbb{N}\)
\(a_{n+1} = a_{n} + 2,\ n\in\mathbb{N}\)