A sequence of 10 integers is as follows: 2, 4, 8, 16, 32 ... If the re

Series is in GP
1st term, a = 2
ratio, r = 2
10th term, x = a*\(r^9\) = 2*\(2^9\) = 1024
Reciprocal of x = 1/1024
\(\frac{1}{10000}\) < \(\frac{1}{1024}\) < \(\frac{1}{1000}\)
--> 0.0001 < x < 0.001

IMO Option C

Pls Hit Kudos if you like the solution

Tenth term in the GP is ar^9=2^10; X=1/2^10; 1/1024; So Xmust be 0.000something (>1) so IMO C

1/2^10 = 1/1024 would fall under the range ; \(0.0001 < x < 0.001\)
IMO C

Not sure where the question is from, but a sequence question can simply never ask you to "guess" the next values in a sequence only by giving you a list of a few numbers. A sequence beginning 2, 4, 8, 16, 32, ... might be the sequence in which the nth term is 2^n -- that's what it looks like. But it could be an infinite number of other sequences as well. It could be that the nth term is given by this rule:

2^n + (n-1)(n-2)(n-3)(n-4)(n-5)

for example, which is equal to 2^n for the first five terms, and is not equal to 2^n for any other terms. So as the question is written, there's no way to guess what the sequence even is, and no way to answer the question. If this were a real GMAT problem, it would provide an algebraic rule, or a description in words, that lets you work out the tenth term without any potential ambiguity.
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The reciprocal of a number with K digits has K-1 leading zeros (unless it is 10^n, in which case it has K-2 leading zeros).

2^10 = 1024 -> 4 digits.

Therefore n has 3 leading zeros.

Must be C.

Solution:

We see that 2 = 2^1, 4 = 2^2, 8 = 2^3, etc. In other words, the nth term of the sequence is 2^n. Thus, the 10th term is 2^10 = 1,024, and since x is the reciprocal of the 10th term, then x = 1/1,024, which has a value between 1/10,000 = 0.0001 and 1/1,000 = 0.001.

Answer: C

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A sequence of 10 integers is as follows: 2, 4, 8, 16, 32 ... If the reciprocal of the 10th term is x, then x should be in which of the following ranges?


(A) 0.000001<x<0.000010

(B) 0.00001<x<0.00010

(C) 0.0001<x<0.001

(D) 0.001<x<0.010

(E) 0.01<x<0.1

Best approach here is 1/1000 = 0.001

0.001 > 1/1024
1/1024 > 0.00001 = 1/10000

C.
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