Test: Geometric Series - Ambitious

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Question 1:   Which of the following are geometric series?
4,8,16...
3,6,10...
4,8,12...
1 2 , 1 2 , 3 2 ...
Question 2:   Which of the following are geometric series?
1 2 , 1 4 , 1 9 .
1.5,1,0.5...
2,4,9...
9,3,1...
Question 3:   Find a common ratio in the following geometric series: 5,15,45...
r=5
r=3
r=3
r= 1 3
Question 4:   Find the 14 th term in the following geometric series: 12,6,3...
a 14 0.0031
a 14 0.15
a 14 0.0172
a 14 0.00146
Question 5:   Find the sum of the first 5 terms in the following series: 3 1 2 ,7,14,...
S 5 =98.5
S 5 =108.5
S 5 =98
S 5 =102.5
Question 6:   Find the sum of first 14 terms in the following series: 1, 1 4 , 1 16 ,...
S 6 1.29
S 6 1.33
S 6 1.5
S 6 1.66
Question 7:   Find the sum to infinity of the following series: 5 , 5 3 , 5 9 ,...
S =10
S =7 1 2
S =5
S =8 2 3
Question 8:   Find the sum to infinity of the following series: 7, 14 5 , 28 25 ,...
S =6 7 8
S =5
S =5 9 10
S =4 1 2
Question 9:   Find the range of values where the following series has a sum to infinity. 1 2x 3 + 4 x 2 3 8 x 3 27 +...
3 2 <x< 3 2
1<x<1
1 2 <x< 1 2
2 3 <x< 2 3
Question 10:   What is the least number of terms in the geometric series 1,3,9,... , if the sum exceeds 1000 ?
n=6
n=9
n=8
n=7