1003107203
Level:
C
Insert such $3$ numbers between the roots of the equation $x^2-10x-119=0$, so that together with the roots of the equation they form $5$ consecutive arithmetic sequence terms. What is the central term?
$5$
$17$
$6$
$-1$
$-7$
Arithmetic sequences
1003107202
Level:
C
The second term of an arithmetic sequence is $-21$, the fifth term is $21$. How many of the first consecutive terms do we have to add up to get a sum of more than $50$?
$8$
$7$
$6$
$9$
$5$
1003107201
Level:
C
The sum of the first ten terms of an arithmetic sequence with odd subscripts is $190$, the sum of the first ten terms with even subscripts is $230$. Find the first term.
$-17$
$-34$
$5$
$4$
$10$
Fifth Term of Arithmetic Sequence
Submitted by ladislav.foltyn on Fri, 04/19/2019 - 18:11Question:
Find the $5$th term of the given arithmetic sequence, where $a_n$ is its $n$th term, $d$ is its common difference, and $s_n$ is the sum of the first $n$ terms of this sequence.
Sum of Terms of Arithmetic Sequences I
Submitted by ladislav.foltyn on Sat, 02/23/2019 - 13:571003097008
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 $-6$:
\[ \begin{aligned}
s_8&=12 \\
s_{12}&=-6
\end{aligned} \]
\( 5 \)
\( -5 \)
\( 2 \)
\( 1 \)
\( -3 \)
1003097007
Level:
B
Find the common difference of an arithmetic sequence \( \left\{a_n\right\}_{n=1}^{\infty} \), if the sum of the first seven terms is $42$ and $a_{10}=-4a_5$:
\[ \begin{aligned}
s_7&=42 \\
a_{10}&=-4a_5
\end{aligned} \]
\( -3 \)
\( 3 \)
\( 15 \)
\( 2 \)
\( -2 \)
1003097006
Level:
B
Find the sum of the first ten terms of an arithmetic sequence \( \left\{a_n\right\}_{n=1}^{\infty} \), if:
\[ \begin{aligned}
a_1+a_5+a_{10}&=40 \\
a_{10}-a_5-a_1&=24
\end{aligned} \]
\( 140 \)
\( 180 \)
\( 160 \)
\( 320 \)
\( 200 \)
1003097005
Level:
B
Find the square of the first term of an arithmetic sequence \( \left\{a_n\right\}_{n=1}^{\infty} \), if:
\[ \begin{aligned}
a_2^2+a_3^2&=100 \\
a_5+a_7&=0
\end{aligned} \]
\( 100 \)
\( 196 \)
\( 64 \)
\( 169 \)
\( 200 \)
1003097004
Level:
B
Find the third term of an arithmetic sequence \( \left\{a_n\right\}_{n=1}^{\infty} \), if:
\[ \begin{aligned}
2a_{10}-3a_3&=5 \\
5a_5+4a_1&=83
\end{aligned} \]
\( 9 \)
\( 7 \)
\( 1 \)
\( 3 \)
\( 11 \)