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# In a geometric sequence each term is found by multiplying the previous

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In a geometric sequence each term is found by multiplying the previous [#permalink]

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26 Jan 2015, 05:04
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In a geometric sequence each term is found by multiplying the previous term by a constant. If the first and second terms in a geometric sequence are 2x and 4x, what is the 600th term of the sequence?

A. $$2^{599}*x$$

B. $$2^{600}*x$$

C. $$2^{(600x)}$$

D. $$4^{600}*x$$

E. $$4^{599}*x$$

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: In a geometric sequence each term is found by multiplying the previous [#permalink]

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26 Jan 2015, 06:08
hi the ans is B/C... as both B and C are the same
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Re: In a geometric sequence each term is found by multiplying the previous [#permalink]

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26 Jan 2015, 06:19
chetan2u wrote:
hi the ans is B/C... as both B and C are the same

B is 2^600*x and C is 2^(600x). Edited. Thank you.
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Re: In a geometric sequence each term is found by multiplying the previous [#permalink]

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26 Jan 2015, 06:25
in this case ans is B...
constant term is 2..so 600th term is 2x*2^(600-1) which is same as x*2^600
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Re: In a geometric sequence each term is found by multiplying the previous [#permalink]

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26 Jan 2015, 06:36
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Each element is found by multiplying the previous term with a constant, so we can start by dividing the second element by the first element:

$$\frac{4x}{2x}=2$$

Therefore, the constant that each previous term is multiplied with must be 2. Therefore:

$$a_3=8x$$, m]a_4=16x[/m], etc.

We see that $$a_n=2^nx$$

So the 600th element is $$2^{600}x$$

The correct answer must be B.
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Re: In a geometric sequence each term is found by multiplying the previous [#permalink]

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02 Feb 2015, 23:11
2
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$$1st term = 2x = 2^1 * x$$

2nd term $$= 4x = 2^2 * x$$

600th term $$= 2^{600} * x$$
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Re: In a geometric sequence each term is found by multiplying the previous [#permalink]

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26 Mar 2015, 22:27
Isn't the formula for an explicit geometric sequence .... An = A1(r^(n-1))..

in my solution ... my answer was An = X*2^(599)
Because i subtracted the N = 600th term by 1. Please advise!

Thanks.
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Re: In a geometric sequence each term is found by multiplying the previous [#permalink]

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26 Mar 2015, 23:19
sisorayi01 wrote:
Isn't the formula for an explicit geometric sequence .... An = A1(r^(n-1))..

in my solution ... my answer was An = X*2^(599)
Because i subtracted the N = 600th term by 1. Please advise!

Thanks.

hi sisorayi01
you are absolutely correct about the formulae..
but A1 is 2x...
so 599 will again come to 600..
hope it helped
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Re: In a geometric sequence each term is found by multiplying the previous [#permalink]

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27 Mar 2015, 07:26
Im sorry i still don't fully understand. How you get 600 for n-1 in the equation. Thank you.

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Math Expert
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Re: In a geometric sequence each term is found by multiplying the previous [#permalink]

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27 Mar 2015, 08:16
sisorayi01 wrote:
Im sorry i still don't fully understand. How you get 600 for n-1 in the equation. Thank you.

Posted from my mobile device

hi...
as the formula is An = A1(r^(n-1))..
A1=2x , r=2 and n=600...
An=2x*2^(600-1)= 2x*2^(599)=x*2^(600)...
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Re: In a geometric sequence each term is found by multiplying the previous [#permalink]

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30 Dec 2017, 01:34
Bunuel wrote:
In a geometric sequence each term is found by multiplying the previous term by a constant. If the first and second terms in a geometric sequence are 2x and 4x, what is the 600th term of the sequence?

A. $$2^{599}*x$$

B. $$2^{600}*x$$

C. $$2^{(600x)}$$

D. $$4^{600}*x$$

E. $$4^{599}*x$$

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

The correct response is (B).

This abstract question asks for a very large term, so it’s a good opportunity to use the formula for a geometric sequence. Geometric sequences are formed by multiplying each term by a constant. To find the nth term in a geometric sequence use the formula: $$a_n=a_1(r^{n−1})$$, where $$a_1$$ is the first term in the sequence and “n” is the term you’re looking to find.

$$a_n=a_1(r^{n−1})$$

$$a_{600}=2x(r^{n−1})$$

“r” is the ratio, which we can find by dividing the second term by the first term. 4x/(2x) = 2, so r = 2.

$$a_{600}=2x(r^{600−1})$$

$$a_{600}=2x(2^{599})$$

Remember that when we are multiplying by similar bases, we can add the exponents:

$$a_{600}=2^{600}x$$
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Re: In a geometric sequence each term is found by multiplying the previous   [#permalink] 30 Dec 2017, 01:34
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