Test: Arithmetic Series I - Challenging

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Question 1:   Can numbers 1,  2 ,  3   be the terms of an arithmetic progression?
No, unless a 2 = 2 ;  a 3 = 3
No
Yes, anyway
Yes, only in the case when a 1 =1
Question 2:   Find the first term and the difference of the arithmetic progression  ( a n )  if a 5 + a 12 =41;  a 10 + a 14 =62 .
a 1 =2;d=3 
a 1 =4; d=3  
a 1 =2; d=3  
a 1 =9.5; d=4  
Question 3:   What is the value of x when expressions x 2 4,5x+3,3x+2 in this right order form an arithmetic progression?
1 only
8 only
1;8
Question 4:   In which case the equation a 1 × a 4 = a 2 2 works for the terms of an arithmetic sequence?
a 1 =d or d=0
Only if d=0
Only if a 1 =d
It cannot work
Question 5:   In what order should expressions a+b 2 , ab 2 , a 2 + b 2 be put to form an arithmetic sequence?
ab 2 ,   a+b 2 ,   a 2 + b 2
a+b 2 ,   ab 2 ,   a 2 + b 2
Only a+b 2 ,   a 2 + b 2 ,   ab 2
a+b 2 , a 2 + b 2 , ab 2 or ab 2 , a 2 + b 2 , a+b 2
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