Arithmetic sequences

1003047803

Level:

In Duolingo application, every user earns so-called lingots (=virtual currency), providing he or she learns at least $10$ minutes for $10$ consecutive days. For the first $10$ days a user earns $1$ lingot, $2$ lingots for the next ten-day period, $3$ lingots for the following $10$ days (i.e. for the first $30$ days a user earns $6$ lingots), etc. Find the smallest number of days in which a user can accumulate $1000$ lingots.

$450$

$45$

$440$

$44$

$430$

1003047802

Level:

A student solves several math problems every day. How many problems will he solve in $14$ days if he manages to solve $5$ on the first day and then gradually increases the number of problems solved by $2$ a day?

$252$

$140$

$434$

$364$

$70$

1003047801

Level:

A certain type of bamboo grows $1.3\,\mathrm{m}$ per day during the vegetation period. Concerning the fact that it reached a height of $30\,\mathrm{m}$ after twenty days of regular growth, how tall was it at the beginning of the first day?

$4\,\mathrm{m}$

$5.3\,\mathrm{m}$

$2.7\,\mathrm{m}$

$10\,\mathrm{m}$

$4.3\,\mathrm{m}$

1003085210

Level:

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 $6\pi-27\mathrm{e}$.

$\pi$

$\pi+\mathrm{e}$

$\pi-\mathrm{e}$

$\pi-2\mathrm{e}$

$\mathrm{e}-\pi$

1003085209

Level:

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.

$0.8$

$0.3$

$0.35$

$-0.1$

$-0.5$

1003085208

Level:

Given an arithmetic sequence $(a_n)_{n=1}^{\infty}$, where $a_8=\frac83$, $a_k=8$ and the common difference is $\frac23$, find $k$.

$16$

$15$

$14$

$21$

$10$

1003085207

Level:

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 $k$.

$15$

$11$

$10$

$9$

$13$

1003085206

Level:

Find the sum of the first $15$ positive terms of the arithmetic sequence: $\left(3n-7\right)_{n=1}^{\infty}$.

$345$

$255$

$238$

$260$

$322$

1003085205

Level:

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 $a_1=-4$.

$264$

$240$

$480$

$-320$

$-352$

1003085204

Level:

Evaluate the sum: $\sum\limits_{n=3}^{15}(-2n+5)$.

$-169$

$299$

$-156$

$-338$

$-312$

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