181k views
4 votes
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
by
7.9k points

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
by
7.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories