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17 Jan 2018, 00:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
64% (01:51) correct
36%
(01:59)
wrong
based on 455
sessions
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For the infinite sequence \(a_1\), \(a_2\), ..., \(a_n\), the value of \(a_n\) is the sum of all previous terms in the sequence from \(a_1\) through \(a_{n−1}\), inclusive. If \(a_n=x\) and \(n>2\), which of the following expresses \(a_{n+2}\) in terms of x?
A. x+2
B. 2x
C. 3x
D. 4x
E. 8X
A. x+2
B. 2x
C. 3x
D. 4x
E. 8X
17 Jan 2018, 00:26
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D
an=x=a1+a2+...a(n-1)
a(n+1)=a1+a2+...+a(n-1)+an=x+x=2x
a(n+2)=a1+a2+...+a(n-1)+an+a(n+1)=x+x+2x=4x
Posted from my mobile device
an=x=a1+a2+...a(n-1)
a(n+1)=a1+a2+...+a(n-1)+an=x+x=2x
a(n+2)=a1+a2+...+a(n-1)+an+a(n+1)=x+x+2x=4x
Posted from my mobile device
13 Sep 2020, 03:20
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Bunuel
Let \(a_1=1\).
Since every value in the sequence is equal to sum of the preceding values, the following sequence is yielded:
\(a_1=1\)
\(a_2=1\)
\(a_3=1+1 = 2\)
\(a_4=1+1+2 = 4\)
\(a_5=1+1+2+4=8\)
Question stem:
If \(a_n=x\) and n>2, which of the following expresses \(a_{n+2}\)?
Let n=3.
Substituting n=3 into the question stem, we get:
If \(a_3=x\), which of the following expresses \(a_5\)?
In the sequence above, \(a_3\) = 2 and \(a_5\) = 8.
When x=2, the correct answer must yield a value of 8.
Only D works:
\(4x=4*2=8\)
