等差数列｛an｝的前n项和为Sn,若S16－S5＝165,则a8＋a9＋a16的值为多少

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等差数列｛an｝的前n项和为Sn,若S16－S5＝165,则a8＋a9＋a16的值为多少
等差数列｛an｝的前n项和为Sn,若S16－S5＝165,则a8＋a9＋a16的值为多少

等差数列｛an｝的前n项和为Sn,若S16－S5＝165,则a8＋a9＋a16的值为多少
a11=15 因为8+9+16=33=3*11 a8＋a9＋a16=3*a11=45或
a8＋a9＋a16=-a11+a13+a14+a8+a9=-a11+2a11+2a11=3a11=45

S16=16*a1+15*16d/2 S5=5*a1+4*5d/2 两式相减有11*a1+110d=165,
a1+10d=15,即a11=15.
又a8+a9+a16=(a1+7d)+(a1+8d)+(a1+15d)=3*a1+30d=3(a1+10d)=3*a11=45

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