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40, 10, 5/2 5/8... (fractions) is it arithmetic or geometric and what are the next two terms PLZ HELP DUE IN 10 MINS

User Pkpk
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1 Answer

1 vote

Answer:

Please check the explanation.

Explanation:

Given the sequence


40,\:10,\:(5)/(2),\:(5)/(8)

A geometric sequence has a constant ratio 'r' and is defined by


\:a_n=a_0\cdot r^(n-1)

Computing the ratios of all the adjacent terms


(10)/(40)=(1)/(4),\:\quad ((5)/(2))/(10)=(1)/(4),\:\quad ((5)/(8))/((5)/(2))=(1)/(4)

The ratio of all the adjacent terms is the same and equal to


r=(1)/(4)

Thus, the given sequence is a geometric sequence.

As the first element of the sequence is


a_1=40

Therefore, the nth term is calculated as


\:a_n=a_0\cdot r^(n-1)


a_n=40\left((1)/(4)\right)^(n-1)

Put n = 5 to find the next term


a_5=40\left((1)/(4)\right)^(5-1)


a_5=40\cdot (1)/(4^4)


a_5=(40)/(4^4)


=(2^3\cdot \:5)/(2^8)


a_5=(5)/(2^5)


a_5=(5)/(32)

now, Put n = 6 to find the 6th term


a_6=40\left((1)/(4)\right)^(6-1)


a_6=40\cdot (1)/(4^5)


a_6=(40)/(4^5)


=(2^3\cdot \:5)/(2^(10))


a_6=(5)/(2^7)


a_6=(5)/(128)

Thus, the next two terms of the sequence 40, 10, 5/2, 5/8... is:


  • a_5=(5)/(32)

  • a_6=(5)/(128)
User Zaph
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