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# In a geometric sequence, each term is a constant multiple of the pre

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In a geometric sequence, each term is a constant multiple of the pre  [#permalink]

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12 Mar 2020, 04:49
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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

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In a geometric sequence, each term is a constant multiple of the pre  [#permalink]

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12 Mar 2020, 04:58
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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

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

Cheers,
Brent
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Re: In a geometric sequence, each term is a constant multiple of the pre  [#permalink]

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12 Mar 2020, 05:00
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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

$$T_4 = -16$$

$$T_3 = 8$$

I.e. previous term is obtained by dividing the available term by -2

I.e.$$T_2 = 8/-2 = -4$$

I.e.$$T_1 = -4/-2 = 2$$

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Re: In a geometric sequence, each term is a constant multiple of the pre  [#permalink]

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15 Mar 2020, 03:44
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

Since 8 must be multiplied by -2 to obtain -16, the constant multiple is -2. Going backward, the 2nd term is 8 / (-2) = -4, and therefore, the first term is (-4) / (-2) = 2.

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Re: In a geometric sequence, each term is a constant multiple of the pre   [#permalink] 15 Mar 2020, 03:44