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【简答题】
记公差d≠0的等差数列{a n }的前n项和为S n ，已知a 1 =2+ 2 ，S 3 =12+3 2 ． （1）求数列{a n }的通项公式a n 及前n项和S n ； （2）记b n =a n - 2 ，若自然数n 1 ，n 2 ，…，n k ，…满足1≤n 1 ＜n 2 ＜…＜n k ＜…，并且b n 1 ，b n 2 ，…，b n k ，…成等比数列，其中n 1 =1，n 2 =3，求n k （用k表示）； （3）试问：在数列{a n }中是否存在三项a r ，a s ，a t （r＜s＜t，r，s，t∈N * ）恰好成等比数列？若存在，求出此三项；若不存在，请说明理由．
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举一反三
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B.
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