1003085205
Level:
B
Find the sum of the $10$th up to $20$th term of an arithmetic sequence given by: $a_{n+1}=a_n+2$ for all $n\in\mathbb{N}$ and $a_1=-4$.
$264$
$240$
$480$
$-320$
$-352$
Arithmetic sequences
1003085206
Level:
B
Find the sum of the first $15$ positive terms of the arithmetic sequence: $\left(3n-7\right)_{n=1}^{\infty}$.
$345$
$255$
$238$
$260$
$322$
1003085207
Level:
B
Given an arithmetic sequence $\{a_n\}_{n=1}^{\infty}$, where $a_5=\frac{11}2$, $a_{10}=-2$ and $s_k=a_1+\dots+a_k=15$, find $k$.
$15$
$11$
$10$
$9$
$13$
1003085209
Level:
B
The sum of the $2$nd and the $4$th term of an arithmetic sequence is $1.2$, the sum of the first $10$ terms is $3.5$. Find the first term.
$0.8$
$0.3$
$0.35$
$-0.1$
$-0.5$
1003085210
Level:
B
The common difference of an arithmetic sequence $\{a_n\}_{n=1}^{\infty}$ is $-\mathrm{e}$. Find the second term, if the sum of the $4$th term up to $9$th term is $6\pi-27\mathrm{e}$.
$\pi$
$\pi+\mathrm{e}$
$\pi-\mathrm{e}$
$\pi-2\mathrm{e}$
$\mathrm{e}-\pi$
1003097001
Level:
B
Find the first term of an arithmetic sequence \( \left\{a_n\right\}_{n=1}^{\infty} \), if:
\[\begin{aligned}
a_2+a_9&=24 \\
a_8-a_6&=4
\end{aligned} \]
\( 3 \)
\( 6 \)
\( 2 \)
\( 10 \)
\( 1 \)
1003097002
Level:
B
Find the common difference of an arithmetic sequence \( \left\{a_n\right\}_{n=1}^{\infty} \), if:
\[ \begin{aligned}
a_{11}+a_4&=-19 \\
a_6+a_7&=-13
\end{aligned} \]
\( -3 \)
\( 3 \)
\( 7 \)
\( -1 \)
\( 10 \)
1003097003
Level:
B
Find the sum of the first five terms of an arithmetic sequence \( \left\{a_n\right\}_{n=1}^{\infty} \), if:
\[ \begin{aligned}
a_1\cdot a_4&=100 \\
a_2+a_6&=10
\end{aligned} \]
\( 50 \)
\( 0 \)
\( 20 \)
\( -5 \)
\( 90 \)
1003097004
Level:
B
Find the third term of an arithmetic sequence \( \left\{a_n\right\}_{n=1}^{\infty} \), if:
\[ \begin{aligned}
2a_{10}-3a_3&=5 \\
5a_5+4a_1&=83
\end{aligned} \]
\( 9 \)
\( 7 \)
\( 1 \)
\( 3 \)
\( 11 \)
1003097005
Level:
B
Find the square of the first term of an arithmetic sequence \( \left\{a_n\right\}_{n=1}^{\infty} \), if:
\[ \begin{aligned}
a_2^2+a_3^2&=100 \\
a_5+a_7&=0
\end{aligned} \]
\( 100 \)
\( 196 \)
\( 64 \)
\( 169 \)
\( 200 \)