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505-555 Level|   Sequences|      
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In a geometric sequence each term is found by multiplying the previous 26 Jan 2015, 06:04
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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. \(4^{599}*x\)


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B
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In a geometric sequence each term is found by multiplying the previous 26 Jan 2015, 07:08
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hi the ans is B/C... as both B and C are the same
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In a geometric sequence each term is found by multiplying the previous 26 Jan 2015, 07:19
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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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In a geometric sequence each term is found by multiplying the previous 26 Jan 2015, 07:25
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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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In a geometric sequence each term is found by multiplying the previous 26 Jan 2015, 07:36
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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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In a geometric sequence each term is found by multiplying the previous 03 Feb 2015, 00:11
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Answer = B. 2^600*x

\(1st term = 2x = 2^1 * x\)

2nd term \(= 4x = 2^2 * x\)

600th term \(= 2^{600} * x\)
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In a geometric sequence each term is found by multiplying the previous 26 Mar 2015, 23:27
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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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In a geometric sequence each term is found by multiplying the previous 27 Mar 2015, 00:19
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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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In a geometric sequence each term is found by multiplying the previous 27 Mar 2015, 08:26
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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
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In a geometric sequence each term is found by multiplying the previous 27 Mar 2015, 09:16
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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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In a geometric sequence each term is found by multiplying the previous 30 Dec 2017, 02:34
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Bunuel
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. \(4^{599}*x\)


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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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In a geometric sequence each term is found by multiplying the previous 07 Feb 2022, 08:16
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