Arithmetic sequences

2010000210

Level: 
C
Insert \(3\) numbers between the roots of the equation \( 5x^2 -26x+5=0\) such that the resulting sequence is a part (\(5\) terms) of an increasing arithmetic sequence with the common difference \(d\). Choose the incorrect statement about the common difference \(d\).
\(d\) is a fraction smaller than \(1\)
\( d>0\)
\(d\) is a fraction greater than \(1\)
\(d\) is a rational number

2010000209

Level: 
C
Insert \(3\) numbers between the roots of the equation \( 4x^2 -17x+4=0\) such that the resulting sequence is a part (\(5\) terms) of an increasing arithmetic sequence with the common difference \(d\). Choose the incorrect statement about the common difference \(d\).
\(d\) is a fraction greater than \(1\)
\( d>0\)
\(d\) is a fraction smaller than \(1\)
\(d\) is a rational number

2010000202

Level: 
B
The \( 5 \)th term of an arithmetic sequence is \( -100 \) and the common difference is \( 4 \). Choose the correct statement about the sum of the first \( 50 \) terms.
\( s_{50} = -900 \)
\( s_{50} < -900 \)
\( s_{50} < 0 \) and \( s_{50} > -900 \)
\( s_{50} > 0 \) and \( s_{50} < 900 \)
\( s_{50} > 900 \)