设公差为-2的等差数列,若a1+a4+a7+…+a97= 50,那么a3+a6+a9+…+a99=?

问题描述:

设公差为-2的等差数列,若a1+a4+a7+…+a97= 50,那么a3+a6+a9+…+a99=?

a1,a4...a97,一共33项,a3,a6,...,a99,也是33项.
a3=a1+2d
a6=a4+2d
...
a99=a97+2d
a3+a6+...+a99=(a1+a4+...+a97)+33*2d
=50+33*2*(-2)
=-82