等差数列《An》中,S12=354,前12项中奇数项与偶数项的和之比为33比27.求公差d!

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等差数列《An》中,S12=354,前12项中奇数项与偶数项的和之比为33比27.求公差d!
等差数列《An》中,S12=354,前12项中奇数项与偶数项的和之比为33比27.求公差d!

等差数列《An》中,S12=354,前12项中奇数项与偶数项的和之比为33比27.求公差d!
有一等差数列{an},其前12项和为354,且其前12项中偶数项的和与奇数项的和的比为32∶27,求公差d．
S偶/S奇=32/27,S12=354
S12=S偶+S奇=354
S12=S偶＋S奇=354．
∵S奇＝162．S偶＝192．
S奇=a1＋a3＋a5＋a7＋a9＋a11
S偶=a2＋a4＋a6＋a8＋a10＋a12
S偶－S奇=(a2＋a4＋a6＋a8＋a10＋a12)－(a1＋a3＋a5＋a7＋a9＋a11)
=(a2－a1)＋(a4－a3)＋(a6－a5)＋(a8－a7)＋(a10－a9)＋(a12－a11)=6d
所以d＝5

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