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7nadin3 [17]
3 years ago
9

The second term in a geometric sequence is 20. The fourth term in the same sequence is 11.25. What is the common ratio

Mathematics
1 answer:
damaskus [11]3 years ago
3 0
Let a_n be the n'th term of the sequence.

so a_1 is the first term, a_2 the second term and so on...

In a geometric sequence with a_1=c, and common ratio r, the terms are as follows:

a_1=c
a_2=cr
a_3=c r^{2}
a_4=c r^{3}
.
.
that is, each term is its previous term times the common ratio r.

In our example

a_2=cr=20 and a_4=c r^{3}=11.25

\frac{a_2}{a_4}= \frac{cr}{c r^{3}}= \frac{1}{ r^{2}}= \frac{20}{11.25}= 1.778

so r^{2} =1/1.778=0.56

r= \sqrt{0.56}= 0.75


Answer: r=0.75
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