设{Xn}是公差为-2的等差数列若X1+X4+X7+……+X97=50，则X3+X6+X9+……+X99=

设X3+X6+X9+……+X99=a
X1+X4+X7+……+X97=50
俩式相减得：（X3-X1）+（X6-X4）+（X9-X7）+……+（X99-X97）=a-50
公差为-2，
X3-X1=X6-X4=X9-X7=……=X99-X97=(-2)x2=-4
所以33x(-4)=a-50
a=-82

解：
X1 + X97 = X4 + X94 = X7 + X91 =...= X46 + X52 = 2*X49
另外还有一个X49

所以 X1+X4+X7+……+X97 = 2*16*X49 + X49 = 33*X49 = 50

X3 + X99 = X6 + X96 = X9 + X93 =...= X48 + X54 = 2*X51
另外还有一个X51

所以 X3+X6+X9+……+X99 = 2*16*X51 + X51 = 33*X51

因为d = -2
所以X51 = X49 + 2d = X49 - 4
所以33*X51 = 33*(X49 -4 ) = 33*X49 -33*4 = -82

原来楼上已经对了的。。。- - !