# Test: Arithmetic Series I - Ambitious

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Question 1:   Find the formula of the n-th term of an arithmetic progression $\text{\hspace{0.17em}}\left({b}_{n}\right)\text{\hspace{0.17em}}$ :
${b}_{n}=a+2n+1$
${b}_{n}=a-2n+1$
${b}_{n}=a-2n+4$
Question 2:   In the arithmetic progression ($\text{\hspace{0.17em}}{a}_{n}\text{\hspace{0.17em}}$ ): $\text{\hspace{0.17em}}{a}_{1}=1;\text{\hspace{0.17em}}d=2.5\text{\hspace{0.17em}}$ . Is $\text{\hspace{0.17em}}13.5\text{\hspace{0.17em}}$ a term of this progression? If yes, find its number.
$n=13$
$n=5$
$13.5\text{\hspace{0.17em}}$ is not a term of this progression
$n=6$
Question 3:   Find the initial term of the arithmetic sequence ($\text{\hspace{0.17em}}{a}_{n}\text{\hspace{0.17em}}$ ), if .
More data is needed
${a}_{1}=23$
${a}_{1}=26$
${a}_{1}=19$
Question 4:   What is the number of the first positive term of an arithmetic sequence ($\text{\hspace{0.17em}}{a}_{n}\text{\hspace{0.17em}}$ ): $-10.2;-9.5;-8.8;$…?
$n=16$
$n=15$
$n=14$
$n=10$
Question 5:   Find the first negative term of an arithmetic sequence ($\text{\hspace{0.17em}}{a}_{n}\text{\hspace{0.17em}}$ ): $\text{\hspace{0.17em}}7.2;\text{\hspace{0.17em}}6.6;\text{\hspace{0.17em}}6\text{\hspace{0.17em}}$ .
$-0.1$
$-1.8$
$-0.6$
$-1.2$
Question 6:   Find the fourth term of an arithmetic progression ($\text{\hspace{0.17em}}{a}_{n}\text{\hspace{0.17em}}$ ) if .
${a}_{4}=-2$
${a}_{4}=-1.5$
${a}_{4}=-3$
${a}_{4}=0$
Question 7:   The formula of an arithmetic progression ($\text{\hspace{0.17em}}{a}_{n}\text{\hspace{0.17em}}$ ) is $\text{\hspace{0.17em}}{a}_{n}=-2n+1\text{\hspace{0.17em}}$. Find the sum of the first twenty terms of this progression.
${s}_{20}=-800$
${s}_{20}=380$
${s}_{20}=-200$
${s}_{20}=-400$
Question 8:   Find the sum of first fifteen terms of an arithmetic sequence ($\text{\hspace{0.17em}}{a}_{n}\text{\hspace{0.17em}}$ ), if $\text{\hspace{0.17em}}{a}_{10}=44;\text{\hspace{0.17em}}d=4\text{\hspace{0.17em}}$ .
${s}_{15}=510$
${s}_{15}=540$
${s}_{15}=1080$
${s}_{15}=504$
Question 9:   How many times ($\text{\hspace{0.17em}}N\text{\hspace{0.17em}}$ ) a clock would stroke during a day if it strokes only integer amount of hours from $\text{\hspace{0.17em}}1\text{\hspace{0.17em}}$ to $\text{\hspace{0.17em}}12\text{\hspace{0.17em}}$ ?
$N=156$
$N=24$
$N=12$
$N=78$
Question 10:   Find the sum of all two-digit numbers that are multiples of $\text{\hspace{0.17em}}6\text{\hspace{0.17em}}$ .
$810$
$1620$
$804$
$816$