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solong [7]
3 years ago
5

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

Mathematics
1 answer:
patriot [66]3 years ago
7 0

Answer:

Please check the explanation.

Step-by-step explanation:

Given the sequence

40,\:10,\:\frac{5}{2},\:\frac{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

\frac{10}{40}=\frac{1}{4},\:\quad \frac{\frac{5}{2}}{10}=\frac{1}{4},\:\quad \frac{\frac{5}{8}}{\frac{5}{2}}=\frac{1}{4}

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

r=\frac{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(\frac{1}{4}\right)^{n-1}

Put n = 5 to find the next term

a_5=40\left(\frac{1}{4}\right)^{5-1}

a_5=40\cdot \frac{1}{4^4}

a_5=\frac{40}{4^4}

   =\frac{2^3\cdot \:5}{2^8}

a_5=\frac{5}{2^5}

a_5=\frac{5}{32}

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

a_6=40\left(\frac{1}{4}\right)^{6-1}

a_6=40\cdot \frac{1}{4^5}

a_6=\frac{40}{4^5}

    =\frac{2^3\cdot \:5}{2^{10}}

a_6=\frac{5}{2^7}

a_6=\frac{5}{128}

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

  • a_5=\frac{5}{32}
  • a_6=\frac{5}{128}
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