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The second and eighth terms of a geometric sequence are 3 and 192, respectively. find the first term, common ratio, and an explicit rule for the nth term.
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The second and eighth terms of a geometric sequence are 3 and 192, respectively. find the first term, common ratio, and an explicit rule for the nth term.
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Jan 21, 2019
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The second and eighth terms of a geometric sequence are 3 and 192, respectively. find the first term, common ratio, and an explicit rule for the nth term.
Mathematics
college
Harish Kommuri
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Harish Kommuri
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To solve the question we proceed as follows:
The explicit formula for geometric series is given by:
nth=ar^(n-1)
where:
a=first term
n=number of terms
second term is:
3=ar(2-1)
3=ar
thus
a=3/r
also the 8th term will be:
192=ar^(8-1)
192=ar^7
substituting the value of a in the above we get:
192=(3/r)r^7
this will give us
64=r^6
thus
r=2
hence the value of a will be:
a=3/2=1.5
Myrtho
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Jan 25, 2019
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Myrtho
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