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TheAnuja55
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p, r, s, t, u
An arithmetic sequence is a sequence in which each term after the first term is equal to the sum of the preceding term and a constant. If the list of numbers shown above is an arithmetic sequence, which of the following must also be an arithmetic sequence?
1.) 2p, 2r, 2s, 2t, 2u
2.) p-3, r-3, s-3, t-3, u-3
3.) p square, r square, s square, t square, u square.
(A)1 only
(B)2 only
(C)3 only
(D)1 and 2
(E)2 and 3
Here constant c such that:
p+c=r, and r+c=s, and s+c=t, and t+c=u.
Rewriting this, there is a constant c such that
c=r-p=s-r=t-s=u-t
1. C1=2r-2p=2s-2r=2t-2s=2u-2t
therefore, C1=2c
Hence this is not true.
2. C2=(r-3)-(p-3)=(s-3)-(r-3)=(t-3)-(s-3)=(u-3)-(t-3)
Clearly, (r-3)-(p-3) = r-p = c
Hence this is true as well
3. C3=(r^2)-(p^2)=(s^2)-(r^2)=(t^2)-(s^2)=(u^2)-(t^2)
The answer here is NO.
Since, if we take (r^2)-(p^2). We know that r=p+c, so r^2=p^2 + 2pc + c^2. That means (r^2)-(p^2) = 2pc + c^2.
So I do have 2 questions:
1. Why the answer is D?
2. Is there any easy way to solve such question?
An arithmetic sequence is a sequence in which each term after the first term is equal to the sum of the preceding term and a constant. If the list of numbers shown above is an arithmetic sequence, which of the following must also be an arithmetic sequence?
1.) 2p, 2r, 2s, 2t, 2u
2.) p-3, r-3, s-3, t-3, u-3
3.) p square, r square, s square, t square, u square.
(A)1 only
(B)2 only
(C)3 only
(D)1 and 2
(E)2 and 3
Here constant c such that:
p+c=r, and r+c=s, and s+c=t, and t+c=u.
Rewriting this, there is a constant c such that
c=r-p=s-r=t-s=u-t
1. C1=2r-2p=2s-2r=2t-2s=2u-2t
therefore, C1=2c
Hence this is not true.
2. C2=(r-3)-(p-3)=(s-3)-(r-3)=(t-3)-(s-3)=(u-3)-(t-3)
Clearly, (r-3)-(p-3) = r-p = c
Hence this is true as well
3. C3=(r^2)-(p^2)=(s^2)-(r^2)=(t^2)-(s^2)=(u^2)-(t^2)
The answer here is NO.
Since, if we take (r^2)-(p^2). We know that r=p+c, so r^2=p^2 + 2pc + c^2. That means (r^2)-(p^2) = 2pc + c^2.
So I do have 2 questions:
1. Why the answer is D?
2. Is there any easy way to solve such question?
