Test: Geometric Series I - Challenging

Double click on maths expressions to zoom
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.
38
3.8
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
128
16
64
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 =0.2 , 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 =2 3 , 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 1 165.4; r= 1 4
a 1 147.3; r= 1 8
a 1 =96;r= 1 2  
a 1 =24; r=2
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.
3, 7, 11
2, 7, 12
1, 7, 49
5, 10, 20
Question 6:   The sum of three sequent numbers that make up a geometric series b n is 65 . If you subtract 1 from the first one and 19 from the second one, you get an arithmetic series a n . Find the sequence of these initial numbers.
3;5;75 
45;15;5
5;15;45 or 45;15;5
5;15;45
Question 7:   For any natural n , the sum of the first n terms of a geometric series b n is given by a formula S n =6 1 2 n 1 . Find the fourth term of this progression.
45 8
9 16
1.125
9 8
Question 8:   Find the sum of squares of six first terms of a geometric series a n with the first term a 1 =2 3 and a common ratio r= 3 .
2028× 3 +1 2
4368
1452
13116 
Question 9:   Find the sum of cubes of the first four terms of a geometric series b n if b 1 =3; b 2 =6 .
12285
3375 
1539
15795
Question 10:   Find the sum of the infinite geometric series a n if a 2 × a 4 =36;  a 3 + a 5 =8 .
27+9 3   
27+9 3   or  279 3
279 3
27