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In a certain geometric sequence, the first five terms are m, n, o, p,
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31 Aug 2022, 06:19
31 Aug 2022, 06:19
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In a certain geometric sequence, the first five terms are m, n, o, p, and q. If m = ½ and o = 18, the fifth term in the series is
A 6
B 9
C 18
D 108
E 648
A 6
B 9
C 18
D 108
E 648
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
In a certain geometric sequence, the first five terms are m, n, o, p,
[#permalink]
31 Aug 2022, 11:19
31 Aug 2022, 11:19
Solution -
The n-th term of a geometric sequence with first term a and the common ratio r is given by ar^(n-1)
In this geometric sequence, there are five terms - m, n, o, p, and q.
It has also been given that m = ½ and o = 18
We can use the formula now, by considering the 3rd term, i.e., o = 18
Therefore, here n = 3
=> o = mr^(n-1)
=> 18 = ( ½ )r^(3-1)
=> 18 * 2 = r^2
=> 36 = r^2
So, r (common ratio) is 6.
Now, we find the fifth term.
q = mr^(n-1)
=> q = ( ½ )r^(5-1)
=> q = ( ½ )r^4
=> q = ( ½ )(6)^4
=> q = 648
The correct answer choice is E.
The n-th term of a geometric sequence with first term a and the common ratio r is given by ar^(n-1)
In this geometric sequence, there are five terms - m, n, o, p, and q.
It has also been given that m = ½ and o = 18
We can use the formula now, by considering the 3rd term, i.e., o = 18
Therefore, here n = 3
=> o = mr^(n-1)
=> 18 = ( ½ )r^(3-1)
=> 18 * 2 = r^2
=> 36 = r^2
So, r (common ratio) is 6.
Now, we find the fifth term.
q = mr^(n-1)
=> q = ( ½ )r^(5-1)
=> q = ( ½ )r^4
=> q = ( ½ )(6)^4
=> q = 648
The correct answer choice is E.
gmatclubot
In a certain geometric sequence, the first five terms are m, n, o, p, [#permalink]
31 Aug 2022, 11:19
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