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

Question

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 .

chetan2u · Answer

hi the ans is B/C... as both B and C are the same

Bunuel · Answer

B is 2^600*x and C is 2^(600x). Edited. Thank you.

chetan2u · Answer

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

littlewarthog · Answer

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 , etc.

We see that  a_n=2^nx

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

The correct answer must be B.

PareshGmat · Answer

Answer = B. 2^600*x

1st term = 2x = 2^1 * x

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

600th term  = 2^{600} * x

sisorayi01 · Answer

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.

chetan2u · Answer

hi  sisorayi01 
you are absolutely correct about the formulae..
but A1 is 2x...
so 599 will again come to 600..
hope it helped

sisorayi01 · Answer

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

chetan2u · Answer

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)...

Bunuel · Answer

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

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