SOLUTION: determine whether each sequence is arithmetic or geometric, find the explicit rule write it in summation notation, and calculate the sum
A) 1/4, 1, 4,...16384
B)2,7,12,..,77
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-> SOLUTION: determine whether each sequence is arithmetic or geometric, find the explicit rule write it in summation notation, and calculate the sum
A) 1/4, 1, 4,...16384
B)2,7,12,..,77
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Question 974719: determine whether each sequence is arithmetic or geometric, find the explicit rule write it in summation notation, and calculate the sum
A) 1/4, 1, 4,...16384
B)2,7,12,..,77 Answer by Edwin McCravy(20056) (Show Source):
A sequence in arithmetic if any two pairs of succesive terms have the same common difference.
A sequence in geometric if any two pairs of succesive terms have the same common quotient (or ratio).
A) is geometric because 1÷(1/4) = 1×(4/1) = 4 and 4÷1 = 4 = common ratio = r
The formula for the nth term of a geometric sequence is:
where is the first term
and r is the common ratio:
So
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B) is arithmetic because 7-2 = 5 and 12-7 = 5 = common difference = d
The formula for the nth term of an arithmetic sequence is:
where is the first term
and d is the common ratio:
So
Edwin
