# Test: Arithmetic Series I - Challenging

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Question 1:   Can numbers be the terms of an arithmetic progression?
Yes, anyway
No
Yes, only in the case when $\text{\hspace{0.17em}}{a}_{1}=1$
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?
$\varnothing$
$-1;\text{\hspace{0.17em}}8$
$8\text{\hspace{0.17em}}$ only
$-1\text{\hspace{0.17em}}$ only
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 $\text{\hspace{0.17em}}{a}_{1}=d$
${a}_{1}=d\text{\hspace{0.17em}}$ or $\text{\hspace{0.17em}}d=0$
It cannot work
Only if $\text{\hspace{0.17em}}d=0$
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 $\text{\hspace{0.17em}}{\left(a-b\right)}^{2},\text{\hspace{0.17em}}{a}^{2}+{b}^{2},\text{\hspace{0.17em}}{\left(a+b\right)}^{2}$
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