2010000203
Level:
A
Insert five numbers between \(15\) and \(57\) such that the resulting sequence is a part of an arithmetic sequence and find the common difference \(d\).
\( d=7\)
\( d=6\)
\( d=12\)
\( d=-7\)
Arithmetic sequences
2010000204
Level:
A
Insert five numbers between \(3\) and \(33\) such that the resulting sequence is a part of an arithmetic sequence and find the common difference \(d\).
\( d=5\)
\( d=6\)
\( d=-5\)
\( d=\frac{30}{7}\)
2010001001
Level:
A
The \( n \)th term of an arithmetic sequence is \( -70 \), the common difference is \( -6 \) and the first term is \(2\). Find the \(n\).
\( 13\)
\(11\)
\(-11\)
\(-13\)
\(12\)
2010001002
Level:
A
Given an arithmetic sequence $(a_n)_{n=1}^{\infty}$, where $a_5=\frac54$, $a_k=15$ and the common difference is $\frac{11}{4}$, find $k$.
\(10\)
\(-6\)
\(0\)
\(9\)
\( 6\)
2010001004
Level:
A
The picture shows a part of the graph of the arithmetic sequence. What is the thirty-second term?
\( 143\)
\(148\)
\( 32\)
\( 158\)
2010001005
Level:
A
The picture shows a part of the graph of the arithmetic sequence. What is the twenty-third term?
\( -53\)
\(-56\)
\(-62\)
\(-23\)
2010006803
Level:
A
In the picture there are the first four terms of the sequence of patterns that consist of black and white squares. Identify the true statement about the number of squares in these patterns, if you know that exactly one of the given statements is true.
The numbers of black squares in patterns determine an arithmetic sequence with the common difference \(6\).
The numbers of white squares in patterns determine an arithmetic sequence with the common difference \(6\).
The numbers of white squares in patterns determine an arithmetic sequence with the first term \(2\).
The numbers of black squares in patterns determine an arithmetic sequence with the first term \(2\).
2010006804
Level:
A
In the picture there are the first four terms of the sequence of patterns that consist of black and white squares. Identify the true statement about the number of squares in these patterns, if you know that exactly one of the given statements is true.
The numbers of white squares in patterns determine an arithmetic sequence with the common difference \(4\).
The numbers of black squares in patterns determine an arithmetic sequence with the common difference \(4\).
The numbers of white squares in patterns determine an arithmetic sequence with the third term \(16\).
The numbers of black squares in patterns determine an arithmetic sequence with the third term \(16\).
2010006805
Level:
A
The picture shows first three patterns formed by dots. The numbers of dots in patterns correspond to terms of an arithmetic sequence. To which term corresponds a pattern that will use \(28\) dots?
Nineth
Eighth
Seventh
Tenth
2010006806
Level:
A
The picture shows first three patterns formed by dots. The numbers of dots in patterns correspond to terms of an arithmetic sequence. To which term corresponds a pattern that will use \(41\) dots?
Tenth
Eighth
Seventh
Nineth