Arithmetic sequences

1003097008

Level: 
B
Find the first term of an arithmetic sequence \( \left\{a_n\right\}_{n=1}^{\infty} \), if the sum of the first eight terms is $12$ and the sum of the first twelve terms is $-6$: \[ \begin{aligned} s_8&=12 \\ s_{12}&=-6 \end{aligned} \]
\( 5 \)
\( -5 \)
\( 2 \)
\( 1 \)
\( -3 \)

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 \( s_{50} < 900 \)
\( s_{50} > 900 \)