Test: Geometric Series I - Challenging

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Question 1:   In the geometric series   a n   it’s known that   a 10 =2 . Find product of the nineteen first terms of this progression.
3.8
38
2 10
2 19
Question 2:   The second term of the geometric series is   a 2 =4 . Find the product of three first terms of this progression.
32
64
16
128
Question 3:   Find the initial term and the common ratio of a geometric series   a n , if   a 5 =3 a 3 ;  a 6 − a 2 =48 .
a 1 =2 3   ,  r= 3
a 1 =2 3   ,  r= 3    or    a 1 =−2 3   ,  r=− 3
a 1 =−2 3   ,  r= 3    or    a 1 =2 3   ,  r=− 3  
a 1 =0.2  ,  r= 3
Question 4:   Find the initial term and the common ratio of a geometric sequence which consists of  6  terms. The sum of the first three terms is  168 , the sum of the last three terms is  21  .
a 1 =96; r= 1 2  
a 1 =24; r=2
a 1 ≈165.4; r= 1 4
a 1 ≈147.3; r= 1 8
Question 5:   The sum of three positive sequent numbers that make up an arithmetic series   a n   is  21 . If you add  2, 3, 9  to these numbers, they would make up a geometric series   b n . Find these initial numbers.
1, 7, 49
5, 10, 20
3, 7, 11
2, 7, 12
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