已知数列是以d为公差的等差数列,数列是以q为公比的等比数列. (1)若数列的前n项和为S n ,且a 1 =b 1 =d=2,S 3 <a 1004 +5b 2 -2012,求整数q的值; (2)在(1)的条件下,试问数列中是否存在一项b k ,使得b k 恰好可以表示为该数列中连续p(p∈N,p≥2)项的和?请说明理由; (3)若b 1 =a r ,b 2 =a s ≠a r ,b 3 =a t (其中t>s>r,且(s-r)是(t-r)的约数),求证:数列中每一项都是数列中的项.
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