Comprehension. Let \( a_{n}\&b_{n} \) be the arithmetic sequences each with common difference 2 ...

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Comprehension. Let \( a_{n}\&b_{n} \) be the arithmetic sequences each with common difference 2 such that \( a_{1}b_{1} \& \) let \( c_{n}=\sum_{k=1}^{n} a_{n}, d_{n}=\sum_{k=1}^{n} b_{k} \). Suppose that the point \( A_{n}\left(a_{n}, c_{n}\right) \), \( B_{n}\left(b_{n}, d_{n}\right) \) are all lying on the parabola \( C: y=p x^{2}+q x+r \) where \( p, q, r \) constants.
The value of \( p \) equals
(a) \( 1 / 4 \)
(b) \( 1 / 3 \)
(c) \( 1 / 2 \)
(d) 2
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