The following video gives some 'proof' to the formula for infinite geometric series... Try not to over-complicate this topic. TRUST ME, it will get over-complicated when you get to calculus. For now, go with the plan. :-)
https://youtu.be/wqnpSzEzq1w
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Question 1
1.
Move each sequence to the appropriate type: Arithmetic or Geometric
13.5, 13.75, 14, 14.25, ...
63, 15.75, 3.9375, 0.984375, ...
90, 45, 22.5, 11.25, ...
125, 195, 265, 335,...
Arithmetic Sequence
Geometric Sequence
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Question 2
2.
Find the sum of the infinite geometric series, if it exists.
(just type the answer...if it doesn't exist type 'does not exist')
NOTE: Be sure to use the fraction in your equation..desmos is going to give you a rounded decimal on the x-axis...find the r and use the fraction NOT the decimal or your answer will be off.
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Question 3
3.
Find the sum of the infinite geometric series, if it exists.
(just type the answer as a fraction...if it doesn't exist type 'does not exist')
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Question 4
4.
Find the sum of the infinite geometric series, if it exists.
(just type the answer...if it doesn't exist type 'does not exist')
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Question 5
5.
Find the sum of the infinite geometric series, if it exists.
(just type the answer...if it doesn't exist type 'does not exist')
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Question 6
6.
Find the sum of the infinite geometric series, if it exists.
(just type the answer...if it doesn't exist type 'does not exist')
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Question 7
7.
Given the recursive formula, what is the third term of the sequence?
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Question 8
8.
Write the recursive formula representing the sequence 2, 12, 72, 432,...
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Question 9
9.
Write the recursive formula representing the sequence 7, 11, 15, 19,...
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Question 10
10.
An ampitheater has 36 rows. The first row has 12 seats, the second row has 15 seats, and the third row has 18 seats. Assuming the pattern continues, how many seats are in the ampitheater?
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Question 11
11.
The first row of a movie theater has 21 seats, and each row after the first has two more seats then the row before it. Your Algebra 2/Trig class is planning to take a field trip to the movies and all 35 students want to sit in the same row. Which row will they be seated in?
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Question 12
12.
What is the nth term of the indicated sequence?
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Question 13
13.
What is
for the arithmetic series described?
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Question 14
14.
Find the missing terms in the following series:
? , 7, ??, ???, 13
(sub the p values into the equation)
3
12
5
1
-3
-5
?
??
???
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Question 15
15.
What series is represented by
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Question 16
16.
What is the last term of the following arithmetic sequence?
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Question 17
17.
165 is the ______ term in the arithmetic sequence 30, 45, 60, 75, ...
(find n...just type in the number)
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Question 18
18.
What is the common ratio of the indicated geometric sequence?
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Question 19
19.
Given the sequence:
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Question 20
20.
What is the sum of the following series?
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Question 21
21.
Which is the nth term of the indicated sequence?
(just type in the answer..as a fraction, if necessary)
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Question 22
22.
What is the sum of the following series?
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Question 23
23.
Starting with n=1, select which numbers would be included in the first five terms of the sequence represented by
(just select in the correct answers--note, this is NOT recursive, so just substitute the values of n)
8
19
6
13
23
12
18
3
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Question 24
24.
Find the missing arithmetic means in each sequence (the missing terms)