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Identify the 19th term of a geometric sequence where a1 = 14 and a9 = 358.80. Round the common ratio and 19th term to the nearest hundredth.
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Identify the 19th term of a geometric sequence where a1 = 14 and a9 = 358.80. Round the common ratio and 19th term to the nearest hundredth.
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Dec 13, 2017
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Identify the 19th term of a geometric sequence where a1 = 14 and a9 = 358.80. Round the common ratio and 19th term to the nearest hundredth.
Mathematics
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Arraval
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an = ar^(n-1)
where, an = nth term, n=number of terms, r=common ratio
a = first term
given: a =14, a9= 358.80, n = 9, r=?
an = ar^(n-1)
358.80 = (14)*(r)^(9-1)
358.80 = 14*(r^8)
r^8 = 358.80/14
r^8 = 25.63
r = 1.5 .. . .commonratio
solve for 19th term...
a19=? , n = 19, r = 1.5, a=14
an = ar^(n-1)
a19 = (14)*(1.5)^(18)
a19=14*(1477.89)
a19 = 20 690.49 . . .ans.
hence, 19th term is 20 690.49
Saeed Zhiany
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Dec 16, 2017
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Saeed Zhiany
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geometric sequence
r is the ratio between any 2 succesive terms
we are given
and
sub and solve for r, since we know
divide both sides by 14
take eight root of both sides (put (358.8/14) to the (1/8) power)
1.5=r
sub
hudnretht
Hadi Moshayedi
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Dec 19, 2017
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Hadi Moshayedi
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