Arithmetic and Geometric Sequences–writing rules and finding given term – Flashcards
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Which term of the arithmetic sequence is {1,4,7,...} is 88?
answer
Write a rule: f(x) = 3x - 2 OR y = 3x - 2 Substitute in for f(x) OR y and solve for x 88 is the 30th term
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The common ratio (growth factor) in a geometric sequence is .4 and the 4th term is 2.5. Find the 3rd term.
answer
6.25
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A ball is dropped from a height of 9 feet. The elasticity of the ball is such that it always bounces up one-third the distance it has fallen. How high will the ball bounce back up after the 5th bounce?
answer
1/9 feet
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Telephone poles are stored in a pile with 25 poles in the first layer, 24 in the second, 23 in the third, and so on. How many telephone poles will be in the 12th layer?
answer
14 telephone poles
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Identify as arithmetic or geometric. Then find the common difference or common ratio. 80,40,20,10 ...
answer
Geometric. The common ratio r = 1/2.
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Identify as arithmetic or geometric. Then find the common difference or common ratio. 12, 9, 6, 3 ...
answer
Arithmetic. The common difference d = -3.
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Identify as arithmetic or geometric. Then find the common difference or common ratio. 1, ¹/₂, ¹/₄, ¹/₈, ¹/₁₆, ...
answer
Geometric. The common ratio r = ¹/₂.
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A rabbit population grew in the following pattern for the first four generations: 2, 4, 8, 16, ... If all the rabbits live and the pattern continues, how many rabbits will there be in the 8th generation?
answer
256
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1.) Tell if the following is a geometric or arithmetic sequence. 2.) Write the formula. 3.) Find the 10th term. 13, 9, 5, 1,...,...
answer
1.) arithmetic 2.) y = -4x + 17 OR f(x) = -4x + 17 3.) -23
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1.) Tell if the following is a geometric or arithmetic sequence. 2.) Write the formula. 3.) Find the 10th term. 512, 256, 128...,...
answer
1.) geometric 2.) y= 512 (½)^x-1 OR f(x)= 512 (½)^x-1 3.) ½
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