设等差数列的首项为a,公差为d。
奇数项之和为15,即:
a + (a + 2d) + (a + 4d) + (a + 6d) = 15
4a + 12d = 15
a + 3d = 15/4
a + 3d = 3.75 ...(1)
偶数项之和为30,即:
(a + d) + (a + 3d) + (a + 5d) + (a + 7d) = 30
4a + 12d = 30
a + 3d = 30/4
a + 3d = 7.5 ...(2)
将(1)和(2)相减,消去a,得到:
7.5 3.75 = 3d
3.75 = 3d
d = 3.75 / 3
d = 1.25
所以公差d为1.25。