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12 Mar 2020, 05:49
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In a geometric sequence, each term is a constant multiple of the preceding one. If the third and fourth numbers in the series are 8 and -16, respectively, what is the first term in the sequence?
(A) -32
(B) -4
(C) 2
(D) 4
(E) 64
(A) -32
(B) -4
(C) 2
(D) 4
(E) 64
12 Mar 2020, 05:58
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SajjadAhmad
In a geometric sequence, each term is a constant multiple of the preceding one. If the third and fourth numbers in the series are 8 and -16, respectively, what is the first term in the sequence?
(A) -32
(B) -4
(C) 2
(D) 4
(E) 64
(A) -32
(B) -4
(C) 2
(D) 4
(E) 64
In a geometric sequence, each term is a constant multiple of the preceding one. If the third and fourth numbers in the series are 8 and -16, respectively...
So, if k = the constant multiple, we can write: term4 = (k)(term3)
We get: -16 = (k)(8), which means k = -2
.....what is the first term in the sequence?
Now that we know the value of k, we can find other terms.
For example, we know that term3 = (-2)(term2), which means: 8 = (-2)(term2), which means term2 = -4
Likewise, since term2 = (-2)(term1), we can write: -4 = (-2)(term1), which means term1 = 2
Answer: C
Cheers,
Brent
12 Mar 2020, 06:00
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SajjadAhmad
In a geometric sequence, each term is a constant multiple of the preceding one. If the third and fourth numbers in the series are 8 and -16, respectively, what is the first term in the sequence?
(A) -32
(B) -4
(C) 2
(D) 4
(E) 64
(A) -32
(B) -4
(C) 2
(D) 4
(E) 64
\(T_4 = -16\)
\(T_3 = 8\)
I.e. previous term is obtained by dividing the available term by -2
I.e.\( T_2 = 8/-2 = -4\)
I.e.\( T_1 = -4/-2 = 2\)
Answer: Option C
