1003097003
Level:
B
Find the sum of the first five terms of an arithmetic sequence \( \left\{a_n\right\}_{n=1}^{\infty} \), if:
\[ \begin{aligned}
a_1\cdot a_4&=100 \\
a_2+a_6&=10
\end{aligned} \]
\( 50 \)
\( 0 \)
\( 20 \)
\( -5 \)
\( 90 \)
Arithmetic sequences
1003097002
Level:
B
Find the common difference of an arithmetic sequence \( \left\{a_n\right\}_{n=1}^{\infty} \), if:
\[ \begin{aligned}
a_{11}+a_4&=-19 \\
a_6+a_7&=-13
\end{aligned} \]
\( -3 \)
\( 3 \)
\( 7 \)
\( -1 \)
\( 10 \)
1003097001
Level:
B
Find the first term of an arithmetic sequence \( \left\{a_n\right\}_{n=1}^{\infty} \), if:
\[\begin{aligned}
a_2+a_9&=24 \\
a_8-a_6&=4
\end{aligned} \]
\( 3 \)
\( 6 \)
\( 2 \)
\( 10 \)
\( 1 \)
1003085104
Level:
A
The \( n \)th term of an arithmetic sequence is \( 1-3n \). Find the \( 5 \)th term and the common difference.
\( a_5=-14;\ d=-3 \)
\( a_5=-2;\ d=-3 \)
\( a_5=14;\ d=-3 \)
\( a_5=-14;\ d=3 \)
\( a_5=-2;\ d=3 \)
1003085103
Level:
A
The third term of an arithmetic sequence is \( 3 \) and the common difference is \( 3 \). Find the \(n\)th term.
\( a_n=3n-6 \text{ for all } n\in\mathbb{N} \)
\( a_n=3n-3 \text{ for all } n\in\mathbb{N} \)
\( a_n=3n \text{ for all } n\in\mathbb{N} \)
\( a_n=3n+3 \text{ for all } n\in\mathbb{N} \)
\( a_n=3n+6 \text{ for all } n\in\mathbb{N} \)
1003085102
Level:
A
The first term of an arithmetic sequence is \( 6 \) and the sixth term is \( 1 \). Find the recursive formula for the sequence.
\( a_1=6;\ a_{n+1}=a_n-1 \text{ for all } n\in\mathbb{N} \)
\( a_1=6;\ a_{n+1}=a_n+1 \text{ for all } n\in\mathbb{N} \)
\(a_1=1;\ a_{n+1}=a_n+5 \text{ for all } n\in\mathbb{N} \)
\( a_1=1;\ a_{n+1}=a_n-5 \text{ for all } n\in\mathbb{N} \)
1003085101
Level:
A
The second term of an arithmetic sequence is \( 3 \) and the fourth term is \( -1 \). Find the recursive formula for the sequence.
\( a_1=5;\ a_{n+1}=a_n-2 \text{ for all } n\in\mathbb{N} \)
\( a_1=2;\ a_{n+1}=a_n-2 \text{ for all } n\in\mathbb{N} \)
\( a_1=3;\ a_{n+1}=a_n-1 \text{ for all } n\in\mathbb{N} \)
\( a_1=5;\ a_{n+1}=a_n-4 \text{ for all } n\in\mathbb{N} \)
\( a_1=3;\ a_{n+1}=a_n-4 \text{ for all } n\in\mathbb{N} \)
1003057910
Level:
B
The sum of the first \( n \) terms of an arithmetic sequence is \( 0 \), the common difference is \( 3 \) and the first term is \( -45 \). Find the \( n \).
\( 31 \)
\( 15 \)
\( 30 \)
\( 16 \)
\( 32 \)
1003057909
Level:
B
The \( 2 \)nd term of an arithmetic sequence is \( 100 \) and the common difference is \( -2 \). Choose the correct statement about the sum of the first \( 100 \) terms.
\( s_{100} > 200 \)
\( s_{100} > 0 \) and \( s_{100} < 200 \)
\( s_{100} < 0 \) and \( s_{100} > -100 \)
\( s_{100} < -100 \)
\( s_{100}=0 \)
1003057908
Level:
B
The \( 3 \)rd term of an arithmetic sequence is \( 2 \) and the \( 20 \)th term is \( 53 \). Find the sum of the first \( 13 \) terms.
\( 182 \)
\( 358 \)
\( 364 \)
\( 689 \)
\( 106 \)