# Test: Arithmetic Series I - Challenging

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Question 1:   Can numbers be the terms of an arithmetic progression?
Yes, only in the case when $\text{\hspace{0.17em}}{a}_{1}=1$
No
Yes, anyway
No, unless
Question 2:   Find the first term and the difference of the arithmetic progression  (${a}_{n}$ )  if .
Question 3:   What is the value of $\text{\hspace{0.17em}}x\text{\hspace{0.17em}}$ when expressions $\text{\hspace{0.17em}}{x}^{2}-4,\text{\hspace{0.17em}}5x+3,\text{\hspace{0.17em}}3x+2\text{\hspace{0.17em}}$ in this right order form an arithmetic progression?
$8\text{\hspace{0.17em}}$ only
$-1;\text{\hspace{0.17em}}8$
$-1\text{\hspace{0.17em}}$ only
$\varnothing$
Question 4:   In which case the equation $\text{\hspace{0.17em}}{a}_{1}×{a}_{4}={a}_{2}^{2}\text{\hspace{0.17em}}$ works for the terms of an arithmetic sequence?
Only if $\text{\hspace{0.17em}}d=0$
Only if $\text{\hspace{0.17em}}{a}_{1}=d$
${a}_{1}=d\text{\hspace{0.17em}}$ or $\text{\hspace{0.17em}}d=0$
It cannot work
Question 5:   In what order should expressions $\text{\hspace{0.17em}}{\left(a+b\right)}^{2},\text{\hspace{0.17em}}{\left(a-b\right)}^{2},\text{\hspace{0.17em}}{a}^{2}+{b}^{2}\text{\hspace{0.17em}}$ be put to form an arithmetic sequence?
Only
${\left(a+b\right)}^{2},\text{\hspace{0.17em}}{a}^{2}+{b}^{2},\text{\hspace{0.17em}}{\left(a-b\right)}^{2}\text{\hspace{0.17em}}$ or $\text{\hspace{0.17em}}{\left(a-b\right)}^{2},\text{\hspace{0.17em}}{a}^{2}+{b}^{2},\text{\hspace{0.17em}}{\left(a+b\right)}^{2}$
Question 6:   The sum of the first terms of an arithmetic progression (${a}_{n}$ ) equals $\text{\hspace{0.17em}}450\text{\hspace{0.17em}}$ . Find $\text{\hspace{0.17em}}{a}_{38}\text{\hspace{0.17em}}$ .
$6$
$228$
$225$
Question 7:   Can the sequence with the sum of the first  $n$  terms , be an arithmetic progression?
No, unless  $d<0$
No
Yes
Yes, only if  ${a}_{1}<0$
Question 8:   Find the sum of all the natural numbers that are multiple of $\text{\hspace{0.17em}}4\text{\hspace{0.17em}}$ and less than $\text{\hspace{0.17em}}130\text{\hspace{0.17em}}$ .
$1221$
$2244$
$2112$
$4224$
Question 9:   The initial term of an arithmetic sequence  (${a}_{n}$ )  is $\text{\hspace{0.17em}}{a}_{1}=-9\text{\hspace{0.17em}}$ and its difference $\text{\hspace{0.17em}}d=6\text{\hspace{0.17em}}$.  How many first terms of the progression make the sum $\text{\hspace{0.17em}}S=960\text{\hspace{0.17em}}$ ?
$160$
$-16;20$
$20$
$106$
Question 10:   Which five sequent numbers of an arithmetic progression  (${a}_{n}$ )  $\text{\hspace{0.17em}}3,7,11\dots \text{\hspace{0.17em}}$ make the sum $\text{\hspace{0.17em}}S=135\text{\hspace{0.17em}}$ ?