an = 8a + 1
思路: 构造出一个等比数列
设 an + x = 8 (a + x)
与原关系对比,推出 x = 1/7
an + 1/7 = 8 (a + 1/7)
所以 an + 1/7 是公比为 8 的等比数列
an + 1/7 = (a1 + 1/7) * q^(n-1) = (1 + 1/7)*8^(n-1) = 8^n /7
an = (8^n- 1)/7