Question

(1)已知等差數(shù)列{a_n}的公差為d(d≠0)，且a₃＋a₆＋a₁₀＋a₁₃＝32.若a_m＝8，則m＝________．
(2)設(shè)等差數(shù)列{a_n}的前n項(xiàng)和為S_n，若S₃＝9，S₆＝36，則a₇＋a₈＋a₉＝________．

Answer 1

(1)8(2)45

(1)由等差數(shù)列性質(zhì)，知a₃＋a₆＋a₁₀＋a₁₃＝(a₃＋a₁₃)＋(a₆＋a₁₀)＝2a₈＋2a₈＝4a₈＝32，∴a₈＝8.∴m＝8.
(2)由等差數(shù)列的性質(zhì)，知S₃，S₆－S₃，S₉－S₆成等差數(shù)列，∴2(S₆－S₃)＝S₃＋(S₉－S₆)，
∴a₇＋a₈＋a₉＝S₉－S₆＝2(S₆－S₃)－S₃＝45.