An arithmetic sequence $T$ has first term $a$ and common difference $d$, where $a$ and $d$ are non-zero integers. Property P is: For some positive integer $m$, the sum of the first $m$ terms of the sequence is equal to the sum of the first $2 m$ terms of the sequence. For example, when $a = 11$ and $d = - 2$, the sequence $T$ has property P , because $$11 + 9 + 7 + 5 = 11 + 9 + 7 + 5 + 3 + 1 + ( - 1 ) + ( - 3 )$$ i.e. the sum of the first 4 terms equals the sum of the first 8 terms. Which of the following statements is/are true? I For $T$ to have property P , it is sufficient that $a d < 0$. II For $T$ to have property P , it is necessary that $d$ is even. A neither of them B I only C II only D I and II
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An arithmetic sequence $T$ has first term $a$ and common difference $d$, where $a$ and $d$ are non-zero integers.
Property P is:
For some positive integer $m$, the sum of the first $m$ terms of the sequence is equal to the sum of the first $2 m$ terms of the sequence.
For example, when $a = 11$ and $d = - 2$, the sequence $T$ has property P , because
$$11 + 9 + 7 + 5 = 11 + 9 + 7 + 5 + 3 + 1 + ( - 1 ) + ( - 3 )$$
i.e. the sum of the first 4 terms equals the sum of the first 8 terms.\\
Which of the following statements is/are true?\\
I For $T$ to have property P , it is sufficient that $a d < 0$.\\
II For $T$ to have property P , it is necessary that $d$ is even.
A neither of them\\
B I only\\
C II only\\
D I and II