Test: Geometric Series I - Ambitious

Double click on maths expressions to zoom
Question 1:   Express the term of a geometric progression a 18 through its another term a 12 and its common ratio r .
a 18 = a 12 ×6r
a 18 = a 12 r 6
a 18 = a 12 +6r
a 18 = a 12 × r 6
Question 2:   ( a n ) is a geometric sequence. Put the sign between these two expressions: a 4 × a 21 ?  a 8 × a 17 .
a 4 × a 21 <  a 8 × a 17
a 4 × a 21 =  a 8 × a 17
a 4 × a 21   a 8 × a 17
a 4 × a 21 >  a 8 × a 17
Question 3:   Find the initial term of the geometric sequence ( a n ), if r= 1 2 , a 4 = 1 32 .
4
1 4
1 2
1 8
Question 4:   192 is a term of a geometric sequence: 2 3 , 3, 6, . Find its number.
5
10
6
7
Question 5:   What two numbers should be put between 3 and 192 two create a geometric progression?
12;48
52;103
12;48
66;129
Question 6:   Find the sum of the first four terms of the geometric sequence ( a n ) if a 4 =189,  r=3 .
560 3
3780
70
140
Question 7:   Find the sum of the first six terms of the geometric sequence ( a n ), if a 1 =5, a 5 =125,r>0 .
5 1 620
155 5 +1
155 5 +5
155
Question 8:   Geometric sequence is given by a formula a n =10× 3 n . Find the sum of the first five terms.
2430
1200
2400
900
Question 9:   The common ratio of the geometric progression ( a n ) is r=2 . Find the initial term if the sum of the first four terms equals 60 .
8
4
2
1
Question 10:   Find the sum of the infinite geometric progression ( a n ), if a 2 =18, r= 1 3 .
81
72
27
162