Test: Arithmetic Series I - Challenging

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Question 1:   Can numbers 1,  2 ,  3   be the terms of an arithmetic progression?
No
Yes, only in the case when a 1 =1
No, unless a 2 = 2 ;  a 3 = 3
Yes, anyway
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 =9.5; d=4  
a 1 =2;d=3 
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?
8 only
1;8
1 only
Question 4:   In which case the equation a 1 × a 4 = a 2 2 works for the terms of an arithmetic sequence?
Only if d=0
a 1 =d or d=0
It cannot work
Only if a 1 =d
Question 5:   In what order should expressions a+b 2 , ab 2 , a 2 + b 2 be put to form an arithmetic sequence?
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
ab 2 ,   a+b 2 ,   a 2 + b 2
Question 6:   The sum of the first 75  terms of an arithmetic progression ( a n ) equals 450 . Find a 38 .
225
228
6
  1 6
Question 7:   Can the sequence with the sum of the first   n   terms S n =a× n 2 +b×n  aR,  bR , be an arithmetic progression?
No
Yes, only if   a 1 <0
Yes
No, unless   d<0
Question 8:   Find the sum of all the natural numbers that are multiple of 4 and less than 130 .
2112
2244
1221
4224
Question 9:   The initial term of an arithmetic sequence  ( a n )  is a 1 =9 and its difference d=6 .  How many first terms of the progression make the sum S=960 ?
160
20
16;20
106
Question 10:   Which five sequent numbers of an arithmetic progression  ( a n )   3,7,11 make the sum S=135 ?
19, 24, 26, 31, 35
11, 19, 27, 35, 43
18, 22, 26, 30, 34
19, 23, 27, 31, 35